MATH 1325 FINAL EXAM REVIEW-Lydia Casas

1.

Student: _____________________Date: _____________________

Instructor: 000200010272053448Prof000200010272053448ProfCourse: Math 1325-MASTER

Assignment: MATH 1325 FINAL EXAMREVIEW

Use the graph of the function f shown to estimate the indicated limits and the function value.

a. f(x)limx→0 −

b. f(x)limx→0 +

c. f(x)limx→0

d. f(0)

a. Find the limit.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. (Type an integer.)f(x) =limx→0 −

B. The limit does not exist.

b. Find the limit.


A. (Type an integer.)f(x)limx→0 +

=


c. Find the limit.


A. (Type an integer.)f(x) =limx→0


d. Find the function value.


A. (Type an integer.)f(0) =

B. The function does not have a value.

-2 2 4

x

-2

2

4

y

MATH 1325 FINAL EXAM REVIEW-Lydia Casas https://xlitemprod.pearsoncmg.com/api/v1/print/math

1 of 26 8/1/18, 9:15 AM

2.

3.

Use the graph of the function f shown to estimate the following limits and the function value. Complete parts a through e.

a. Find . Select the correct choice below and, if necessary, fill in the answer box to complete your choice.f(x)limx→2 −

A. (Type an integer.)f(x) =limx→2 −


b. Find . Select the correct choice below and, if necessary, fill in the answer box to complete your choice.f(x)limx→2 +


=


c. Find . Select the correct choice below and, if necessary, fill in the answer box to complete your choice.f(x)limx→2



d. Find the function value . Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

f(2)

A. (Type an integer.)f(2) =

B. The function does not have a value.

e. Is it possible to define so that Choose the correct answer below.f(2) f(x) = f(2)?limx→2

A. No, it is not possible to define so that .f(2) f(x) = f(2)limx→2

B. It is not necessary to define because .f(2) f(x) = f(2)limx→2

C. Yes, it is possible to define so that .f(2) f(x) = f(2)limx→2

Find the limit if it exists.

x(x − 3)limx→8


A. (Simplify your answer.)x(x − 3)limx→8

=


-2 2 4

x

-2

2

4

y


2 of 26 8/1/18, 9:15 AM

4.

5.

Let . Find the indicated quantities, if they exist.f( ) =xx − 6

x2 − 6x

(A) f( )limx→0

x (B) f( )limx→6

x (C) f( )limx→36

x

(A) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. (Type an integer or a simplified fraction.)limx→0

x − 6

x2 − 6x=

B. The limit does not exist.(B) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.


x − 6

x2 − 6x=

B. The limit does not exist.(C) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.


x − 6

x2 − 6x=


Let f(x) . Find the indicated quantities, if they exist.=4x2 − 23x − 6

x2 + 13x − 114

(A) f( )limx→6

x (B) f( )limx→0

x (C) f( )limx→1

x

(A) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.(Type an integer or a simplified fraction.)lim

x→6

4x2 − 23x − 6

x2 + 13x − 114=

B. The limit does not exist.(B) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.


x→0

4x2 − 23x − 6

x2 + 13x − 114=

B. The limit does not exist.(C) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.


x→1

4x2 − 23x − 6

x2 + 13x − 114=



3 of 26 8/1/18, 9:15 AM

6.

7.

8.

Use the given graph to find f(x) limit.limx→ 5 −

A. −∞B. 5C. 0D. ∞

Find the indicated quantities for .f(x) = 3x2

(A) The slope of the secant line through the points ( ,f( )) and ( h,f( h)),1 1 1 + 1 + h ≠ 0(B) The slope of the graph at ( ,f( ))1 1(C) The equation of the tangent line at ( ,f( ))1 1

(A) The slope of the secant line through the points ( ,f( )) and ( h,f( h)), , is .1 1 1 + 1 + h ≠ 0

(B) The slope of the graph at ( ,f( )) is .1 1(Type an integer or a simplified fraction.)

(C) The equation of the tangent line at ( ,f( )) is y .1 1 =

Find and find the equation of the line tangent to the graph of f at x .f (x)′ = 1

f(x) = (2 + 4x)(3 − 2x)

f (x)′ =

y =

-8 -4 4 8

x

-4

-2

2

4

y


4 of 26 8/1/18, 9:15 AM

9.

10.

11.

The revenue (in dollars) from the sale of x car seats for infants is given by the following function.

R(x) = 64x − 0.020x2 0 ≤ x ≤ 3200(A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats.(B) Use the four-step process to find .R (x)′(C) Find the revenue and the instantaneous rate of change of revenue at a production level of 1,000 car seats, and interpret the results.

(A) Find the average change in revenue if production is changed from 1,000 car seats to 1,050 car seats.

(Round to one decimal place as needed.)

(B) R (x)′ =

(C) R(1000) =

R (1000)′ =

Interpret these results. Choose the correct answer below.

A. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is decreasing at a rate of dollars per seat.R (1000)′

B. This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is increasing at a rate of dollars per seat.R (1000)′

C. This means that at a production level of 1,000 car seats, the revenue is dollars and is increasing at a rate of R(1000) dollars per seat.

R (1000)′

The total cost (in dollars) of producing x food processors is C(x) x x .= 1600 + 40 − 0.6 2

(A) Find the exact cost of producing the st food processor.21(B) Use the marginal cost to approximate the cost of producing the st food processor.21

(A) The exact cost of producing the st food processor is $ .21

(B) Using the marginal cost, the approximate cost of producing the st food processor is $ .21

The total cost (in dollars) of manufacturing x auto body frames is C(x) .= 40,000 + 800x

(A) Find the average cost per unit if frames are produced.200(B) Find the marginal average cost at a production level of units.200(C) Use the results from parts (A) and (B) to estimate the average cost per frame if frames are produced.201

(A) If frames are produced, the average cost is $ per frame.200

(B) The marginal average cost at a production level of units is $ per frame.200(Round to the nearest cent as needed.)

(C) Using the results from parts (A) and (B), the estimate of the average cost per frame if frames are produced is $201(Round to the nearest cent as needed.)


5 of 26 8/1/18, 9:15 AM

12. The price-demand equation and the cost function for the production of table saws are given, respectively, by x p and C(x) x, where x is the number of saws that can be sold at a price of $p per saw and C(x)is the total cost (in dollars) of producing x saws. Complete parts (A) through (I) below.

= 12,000 − 40 = 84,000 + 70

(A) Express the price p as a function of the demand x, and find the domain of this function.

The price function is p .=

Determine the domain of this function. Select the correct choice below and fill in the answer box(es) within your choice.

A. x ≤

B. x ≥

C. x <

D. x >

(B) Find the marginal cost.

The marginal cost is .

(C) Find the revenue function and state its domain.

The revenue function is R(x) .=

Determine the domain of this function. Select the correct choice below and fill in the answer box(es) within your choice.

A. x >

B. x ≥

C. x <

D. x ≤

(D) Find the marginal revenue.

The marginal revenue is .

(E) Find ( ) and ( ) and interpret these quantities.R′ 1,500 R′ 4,500Find and interpret ( ). Select the correct choice below and fill in the answer boxes within your choice.R′ 1,500(Simplify your answers.)

A. ( ) ; at a production level of , revenue is increasing at the rate of $ per saw.R′ 1,500 =

B. ( ) ; at a revenue of $ per saw, saw production is increasing at the rate of per dollar.R′ 1,500 =

C. ( ) ; at a revenue of $ per saw, saw production is decreasing at the rate of per dollar.R′ 1,500 =

D. ( ) ; at a production level of , revenue is decreasing at the rate of $ per saw.R′ 1,500 =

Find and interpret ( ). Select the correct choice below and fill in the answer boxes within your choice.R′ 4,500(Simplify your answers.)

A. ( ) ; at a revenue of $ per saw, saw production is increasing at the rate of per dollar.R′ 4,500 =

B. ( ) ; at a production level of , revenue is at R′ 4,500 = decreasing

≤

<

<

≤


6 of 26 8/1/18, 9:15 AM

the rate of $ per saw.

(F) Graph the cost function and the revenue function on the same coordinate system for 0 x . Find the break-evenpoints, and indicate regions of loss and profit. Use light shading for regions of profit and dark shading for regions of loss. Choose the correct graph below.

≤ ≤ 12,000

A.

Break-even points: ( , )

and ( , )

3181.00 701330.32

11619.00 110669.68

B.


and ( , )

381.00 110669.68

8819.00 701330.32

C.


and ( , )

3181.00 701330.32

11619.00 110669.68

D.


and ( , )

381.00 110669.68

8819.00 701330.32

(G) Find the profit function in terms of x.

P(x) =

(H) Find the marginal profit.

The marginal profit is .

(I) Find ( ) and ( ) and interpret these quantities.P′ 1,500 P′ 3,000Find and interpret ( ). Select the correct choice below and fill in the answer boxes within your choice.P′ 1,500(Simplify your answers.)

A. ( ) ; at a production level of saws, profit is decreasing at the rate of $ per saw.P′ 1,500 =

B. ( ) ; at a profit level of $ saw production is increasing at the rate of saws per dollar.P′ 1,500 =

C.

at the rate of saws per dollar.

D. ( ) ; at a production level of saws, profit is increasing at the rate of $ per saw.P′ 1,500 =

Find and interpret ( ). Select the correct choice below and fill in the answer boxes within your choice.P′ 3,000(Simplify your answers.)

A. ( ) ; at a profit level of $ saw production is decreasing at the rate of saws per dollar.P′ 3,000 =

B. ( ) ; at a profit level of $ saw production is increasing at the rate of saws per dollar.P′ 3,000 =

C. saws, profit is at increasing

0 12000

x0

1M

0.5M

y

0 12000

x0

1M

0.5M

y

0 12000

x0

1M

0.5M

y

0 12000

x0

1M

0.5M

y

( ) ; at a profit level of $ saw production is decreasing P′ 1,500 =

( ) ; at a production level of P′ 3,000 =


7 of 26 8/1/18, 9:15 AM

13.

14.

15.

16.

the rate of $ per saw.

Find the indicated derivative and simplify.

for y′ y =7x − 5

x2 + 2x

y′ =

The total sales of S (in thousands of DVD's) of a certain movie are given by the following formula where t is the number of months since the release of the DVD. Use the formula to answer the questions.

S(t) =70t2

t2 + 150

a) Find .S (t)′

(t)S′ =

b) Find and .S(10) S (10)′

The value of S( ) rounded to the nearest hundredth is .10

The value of rounded to the nearest hundredth is .S (10)′

What do the values for and indicate?S(10) S (10)′

A. After months, the total sales are DVD's and the sales are increasing at the rate of DVD's per month.10 28,000

3.36B. After months, the total sales are DVD's and the sales are increasing at the rate of

DVD's per month.10 28,000

3360C. After months, the total sales are DVD's and the sales are increasing at the rate of

DVD's per month.10 33,600

2800D. After months, the total sales are DVD's and the sales are increasing at the rate of

DVD's per month.10 3360 28

c) Use the results from part (b) to estimate the total sales after months.11

After months, the total sales will be approximately how many DVD's?11

(Round to the nearest whole number.)

Find the indicated derivative and simplify.

for y′ y = 8 + 3x − 9x e2 x

y′ =

Replace ? with an expression that will make the equation valid.

e = eddx

x7 + 9 x7 + 9 ?

The missing expression is .


8 of 26 8/1/18, 9:15 AM

17.

18.

19.

20.

21.

22.

23.

Replace ? with an expression that will make the equation valid.

ln x + 9 =ddx

5 1

x5 + 9?

The missing expression is .

Find .(x)f ′

f(x) = 5x + 43 6

(x)f ′ =

Find (x).f′

f(x) = e 16x

(x)f′ =

Find .(x)f ′

f(x) = 4 e − 2x

(x)f ′ =

Find the derivative.

f(x) = 6 9x2 + 7

(x)f ′ =

Find (x).f′

f(x) = 8 ln 9 + 4x2

(x)f′ =

Use implicit differentiation to find and evaluate at ( , ).y′ y′ − 1 4

02xy + y + 6 =

y′ =

Evaluate at ( , ).y′ − 1 4

y′ ( − 1,4) =(Simplify your answer.)


9 of 26 8/1/18, 9:15 AM

24.

25.

26.

27.

28.

Use a graphing calculator to find the equation(s) of the tangent line(s) at the point(s) on the graph of the equation

, where x .y − xy − x5 5 = 11 = 1

Give the equation of the line that is tangent to the curve at x .= 1

y =(Type your answer in slope-intercept form. Use integers or decimals for any numbers in the expression. Round to two decimal places as needed. Round all intermediate values to two decimal places as needed.)

Use the price-demand equation below to find E(p), the elasticity of demand.

x f(p) p= = 12,500 − 225

E(p) =

Use the price-demand equation equation below to find E(p), the elasticity of demand.

x f(p)= = 3200 − 2p2

E(p) =

Use the price-demand equation below to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p.

x f(p) p= = 1890 − 3 − 0.1p2

(A) p = 25 (B) p = 75 (C) p = 70

(A) Describe the demand's elasticity for the given price-demand equation at p . Choose the correct answer below.= 25

ElasticInelasticUnit Elastic

(B) Describe the demand's elasticity for the given price-demand equation at p . Choose the correct answer below.= 75

Unit ElasticInelasticElastic

(C) Describe the demand's elasticity for the given price-demand equation at p . Choose the correct answer below.= 70

ElasticUnit ElasticInelastic

A rock is thrown into a still pond. The circular ripples move outward from the point of impact of the rock so that the radius of the circle formed by a ripple increases at the rate of feet per minute. Find the rate at which the area is changing at the instant the radius is feet.

36

When the radius is feet, the area is changing at approximately square feet per minute. (Type an integer or a decimal. Round to the nearest thousandth as needed.)

6


10 of 26 8/1/18, 9:15 AM

29.

30.

The radius of a spherical balloon is increasing at the rate of . How fast is the volume changing when the radius is cm?

0.5 cm / minute7.5

The volume is changing at a rate of .cm / minute3

(Type an integer or a decimal. Round to one decimal place as needed.)

Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.

f(x) = x + 6x − 163


A. The function is increasing on .(Type

B. The function is never increasing.


A. The function is decreasing on .(Type

B. The function is never decreasing.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.(Type integers or simplified fractions. Use a comma to separate answers as needed.)

A. The function has local maxima f(c) , and no local minima.=

B. The function has local maxima f(c) and local minima f(c) .= =

C. The function has local minima f(c) , and no local maxima.=

D. The function has no local extrema.

your answer using interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.)

your answer using interval notation. Type integers or simplified fractions. Use a comma to separate answers as needed.)


11 of 26 8/1/18, 9:15 AM

31.

32.

Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema.

f(x) = 2x − 72x + 174 3


A. The function is increasing on .(Type

B. There is no solution.


A. The function is decreasing on .(Type

B. There is no solution.

Which statement regarding the local extrema of the function is true? Choose the correct answer below.

A. The function has a local maximum at x 0.=B. The function has a local maximum at x 0 and a local minimum at = x = 27.C. The function has a local minimum at x = 27.D. The function has a local minimum at x = 0.

Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward,and the inflection points.

f(x) = x + 9x20 2

For what interval(s) of x is the graph of f concave upward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

B. The graph is never concave upward.

For what interval(s) of x is the graph of f concave downward? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A.

B. The graph is never concave downward.

Determine the x coordinates of any inflection points of the graph of f(x). Select the correct choice below and, if necessary,fill in the answer box to complete your choice.

A.

B. There are no inflection points.

your answer using interval notation. Use a comma to separate answers as needed.)

your answer using interval notation. Use a comma to separate answers as needed.)

(Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.)

(Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.)

(Type an exact answer. Use a comma to separate answers as needed.)


12 of 26 8/1/18, 9:15 AM

33. Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of y = f(x).

f(x) = 6x − 11x6 5


A. The domain of f is .(Type

B. The domain of f is empty.


A. The x-intercept(s) of f is/are x .=(Type an exact answer,separate answers as

B. The function f has no x-intercepts.


A. The y-intercept of f is y .=(Type an exact answer,needed.)

B. The function f has no y-intercept.


A. The function f is increasing on the subinterval(s) .(Type

B. The function f is never increasing.


A. The function f is decreasing on the subinterval(s) .(Type

B. The function f is never decreasing.


A. The function f has a local maximum at x .=(Type an exact answer,needed.)

B. The function f has no local maximum.


A. The function f has a local minimum at x .=(Type an exact answer,separate answers as

B. The function f has no local minimum.

your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

using radicals as needed. Type an integer or a fraction. Use a comma to needed.)

using radicals as needed. Use a comma to separate answers as

your answer in interval notation. Type an exact answer, using radicals as needed. Type an integer or a fraction. Use a comma to separate answers as needed.)

your answer in interval notation. Type an exact answer, using radicals as needed. Type an integer or a fraction. Use a comma to separate answers as needed.)

using radicals as needed. Use a comma to separate answers as



13 of 26 8/1/18, 9:15 AM

34.


A. The graph of f is concave upward on the subinterval(s) .(Type your answer in interval notation. Type an exact

B. The function f is never concave upward.


A. The graph of f is concave downward on the subinterval(s) .(Type your answer in interval notation. Type an exact

B. The function f is never concave downward.


A. The function f has an inflection point at x .=(Type an exact answer,separate answers as

B. The function f has no inflection point.

Choose the correct graph of y f(x) below.=

A. B. C. D.

For the graph of shown on the right, find the absolute minimum and the absolute maximum over the interval .

y = f(x)

[6, 10]

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A. The absolute minimum is at x .=

B. There is no absolute minimum.

Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A. The absolute maximum is at x .=

B.

answer, using radicals as needed. Type an integer or a fraction. Use a comma to separate answers as needed.)

answer, using radicals as needed. Type an integer or a fraction. Use a comma to separate answers as needed.)


-4 4

x

-18

18y

-4 4

x

-18

18y

-4 4

x

-18

18y

-4 4

x

-18

18y

0 6 12

x0

5

10f(x)

There is no absolute maximum.


14 of 26 8/1/18, 9:15 AM

35. Find the absolute maximum and minimum, if either exists, for the function on the indicated interval.

f(x) = x − 15x + 63x + 83 2

(A) (B) (C)[ − 1, 8] [ − 1, 7] [5, 8]

(A) Find the absolute maximum. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A. The absolute maximum is at x .=(Use

B. There is no absolute maximum.

Find the absolute minimum. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.

A. The absolute minimum is at x .=(Use


(B) Find the absolute maximum. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.






(C) Find the absolute maximum. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.






a comma to separate answers as needed.)







15 of 26 8/1/18, 9:15 AM

36.

37.

38.

39.

A company manufactures and sells x cellphones per week. The weekly price-demand and cost equations are given below.

and p = 400 − 0.5x C(x) = 25,000 + 130x

(A) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly revenue? What is the maximum weekly revenue?

The company should produce phones each week at a price of $ .(Round to the nearest cent as needed.)

The maximum weekly revenue is $ . (Round to the nearest cent as needed.)

(B) What price should the company charge for the phones, and how many phones should be produced to maximize the weekly profit? What is the maximum weekly profit?

The company should produce phones each week at a price of $ .(Round to the nearest cent as needed.)

The maximum weekly profit is $ . (Round to the nearest cent as needed.)

A company manufactures and sells x television sets per month. The monthly cost and price-demand equations are

C(x) and , 0 x .= 74,000 + 80x p(x) = 250 −x

20≤ ≤ 5000

(A) Find the maximum revenue.(B) Find the maximum profit, the production level that will realize the maximum profit, and the price the company should charge for each television set.(C) If the government decides to tax the company $ for each set it produces, how many sets should the company manufacture each month to maximize its profit? What is the maximum profit? What should the company charge for eachset?

4

(A) The maximum revenue is $ .(Type an integer or a decimal.)

(B) The maximum profit is $ when sets are manufactured and sold for $ each.(Type integers or decimals.)

(C) When each set is taxed at $ , the maximum profit is $ when sets are manufactured and sold for $ each.

4

(Type integers or decimals.)

A manufacturer of hospital supplies has a uniform annual demand for boxes of bandages. It costs $ to store one box of bandages for one year and to set up the plant for production. How many times a year should the company produce boxes of bandages in order to minimize the total storage and setup costs?

80,000 20$500

The company should produce boxes of bandages time(s) a year.

A publishing company sells copies of certain books each year. It costs the company to store each book for a year. Each time it must print additional copies, it costs the company to set up the presses. How many books should the company produce during each printing in order to minimize its total storage and setup costs?

625,000 $1$500

The company should produce books each printing in order to minimize costs.


16 of 26 8/1/18, 9:15 AM

40.

41.

42.

43.

44.

Calculate , given the following.6x dx∫3

5

2

x dx∫

3

4

2 =373

x dx∫4

5

2 =613

xdx∫3

4

=72

6x dx∫3

5

2 =

(Type an integer or a simplified fraction.)

Evaluate the integral.

x + x + 3 dx∫− 3

− 1

2

A. 11.17B. 10.50C. 16.33D. 10.67

Evaluate the integral.

2x − 5x dx∫1

3

3 − 2

A. 36.67B. 47.17C. 50.00D. 60.00

Find the area bounded by the graphs of the indicated equations over the given interval. Compute answers to three decimal places.

y x ; y 0;= − 4 − 8 = − 1 ≤ x ≤ 2

The area, calculated to three decimal places, is square units.

Find the area bounded by the graphs of the indicated equations over the given interval.

y x ; y 0;= 2 − 22 = − 3 ≤ x ≤ 0

The area is square units.


17 of 26 8/1/18, 9:15 AM

45. Find the consumers' surplus and the producers' surplus at the equilibrium price level for the given price-demand andprice-supply equations. Include a graph that identifies the consumers' surplus and the producers' surplus. Round all values to the nearest integer.

p D(x) ; p S(x)= = 70 − 0.07x = = 30 e 0.001x

What is the consumers' surplus, CS?

CS =(Round to the nearest integer as needed. Round all intermediate steps to the nearest integer.)

What is the producers' surplus, PS?

PS =(Round to the nearest integer as needed. Round all intermediate steps to the nearest integer.)

Which one of the following graphs correctly identifies the consumers' surplus and the producers' surplus?

A. B. C.

0 1500

x10

100p

CSPS

S(x)

D(x)

x

P

7000

x

150

10

p

CSPS

S(x)

D(x)

x

P

9500

x

200

10

p

CSPS

S(x)

D(x)

x

P


18 of 26 8/1/18, 9:15 AM

1. A. (Type an integer.)f(x) =limx→0 −

2


= 2


2

A. (Type an integer.)f(0) = 2

2. A. (Type an integer.)f(x) =limx→2 −

− 1


= 2


A. (Type an integer.)f(2) = 2

A. No, it is not possible to define so that .f(2) f(x) = f(2)limx→2

3. A. (Simplify your answer.)x(x − 3)limx→8

= 40

4. B. The limit does not exist.


x − 6

x2 − 6x=

16


x − 6

x2 − 6x=

136

5. A. (Type an integer or a simplified fraction.)limx→6

4x2 − 23x − 6

x2 + 13x − 114= 1


4x2 − 23x − 6

x2 + 13x − 114=

119


4x2 − 23x − 6

x2 + 13x − 114=

14

6. A. −∞


19 of 26 8/1/18, 9:15 AM

7. 6 + 3h

6

6x − 3

8. 8 − 16x

− 8x + 14

9. 23

64 − 0.040x

44,000

24

B.This means that at a production level of 1,000 car seats, the revenue is R(1000) dollars and is increasing at a rate of

dollars per seat.R (1000)′

10. 15.40

16

11. 1,000

− 1.00

999.00


20 of 26 8/1/18, 9:15 AM

12. 300 − 0.025x

A. x0 ≤ ≤ 12,000

70

300x − 0.025x2

D. x0 ≤ ≤ 12,000

300 − 0.05x

A.( ) ; at a production level of , revenue is increasing at the rate of

$ per saw.R′ 1,500 = 225.00 1,500

225.00

D.( ) ; at a production level of , revenue is at the rate of

$ per saw.R′ 4,500 = 75.00 4,500 increasing

75.00

D. , ) and ( , )8819.00 701330.32

− 0.025x + 230x − 84,0002

230 − 0.05x

D.( ) ; at a production level of saws, profit is increasing at the rate of

$ per saw.P′ 1,500 = 155.00 1,500

155.00

C.( ) ; at a production level of saws, profit is at the rate of

$ per saw.P′ 3,000 = 80.00 3,000 increasing

80.00

13. − 7x2 + 10x + 10

x2 + 2x 2

14. 21000t

t2 + 150 2

28.00

3.36

B. After months, the total sales are DVD's and the sales are increasing at the rate of DVD's per month.10 28,000 3360

31,360

0 12000

x

Break-even points: (381.00 110669.680

1M

0.5M

y


21 of 26 8/1/18, 9:15 AM

15. e 11 − 15x − 9xx 2

16. 7x6

17. 5x4

18. 90x 5x + 42 3 5

19. 16 e 16x

20. − 8 e − 2x

21. 54x

9x2 + 7

22. 64x

4x2 + 9

23. − 2y2x + 1

8

24. 0.17x + 1.52

25. 9p500 − 9p

26. 2p2

1600 − p2

27. Inelastic

Elastic

Unit Elastic


22 of 26 8/1/18, 9:15 AM

28. 113.097

29. 353.4

30. A. The function is increasing on .( −∞,∞)(Type your answer using interval notation. Type integers or simplified fractions. Use a comma to separate answers asneeded.)

B. The function is never decreasing.

D. The function has no local extrema.

31. A. The function is increasing on .(27,∞)(Type your answer using interval notation. Use a comma to separate answers as needed.)

A. The function is decreasing on .( −∞,27)(Type your answer using interval notation. Use a comma to separate answers as needed.)

C. The function has a local minimum at x = 27.

32. A. ( −∞,∞)(Type your answer in interval notation. Type an exact answer. Use a comma to separate answers as needed.)

B. The graph is never concave downward.

B. There are no inflection points.


23 of 26 8/1/18, 9:15 AM

33. A. The domain of f is .( −∞,∞)(Type your answer in interval notation. Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

A. The x-intercept(s) of f is/are x .= 0,116

(Type an exact answer, using radicals as needed. Type an integer or a fraction. Use a comma to separate answers asneeded.)

A. The y-intercept of f is y .= 0(Type an exact answer, using radicals as needed. Use a comma to separate answers as needed.)

A. The function f is increasing on the subinterval(s) .,∞5536

(Type your answer in interval notation. Type an exact answer, using radicals as needed. Type an integer or a fraction. Use a comma to separate answers as needed.)

A. The function f is decreasing on the subinterval(s) .−∞,5536


B. The function f has no local maximum.

A. The function f has a local minimum at x .=5536


A. The graph of f is concave upward on the subinterval(s) .( −∞,0), ,∞119


A. The graph of f is concave downward on the subinterval(s) .0,119


A. The function f has an inflection point at x .= 0,119


D.

-4 4

x

-18

18y


24 of 26 8/1/18, 9:15 AM

34. A. The absolute minimum is at x .3 = 8

A. The absolute maximum is at x .5 = 10

35. A. The absolute maximum is at x .89 = 3 (Use a comma to separate answers as needed.)

A. The absolute minimum is at x .− 71 = − 1 (Use a comma to separate answers as needed.)

A. The absolute maximum is at x .89 = 3 (Use a comma to separate answers as needed.)

A. The absolute minimum is at x .− 71 = − 1 (Use a comma to separate answers as needed.)

A. The absolute maximum is at x .73 = 5 (Use a comma to separate answers as needed.)

A. The absolute minimum is at x .57 = 7 (Use a comma to separate answers as needed.)

36. 400

200

80,000.00

270

265

11,450.00

37. 312500.00

70,500.00

1700

165.00

63,780.00

1660

167.00

38. 40

39. 25,000

40. 196

41. D. 10.67

42. A. 36.67


25 of 26 8/1/18, 9:15 AM

43. 30

44. 57

45. 4,828

2,851

A. 0 1500

x10

100p

CSPS

S(x)

D(x)

x

P


26 of 26 8/1/18, 9:15 AM

MATH 1325 FINAL EXAM REVIEW-Lydia Casas

Documents

Transcript of MATH 1325 FINAL EXAM REVIEW-Lydia Casas