turunan 3
36
x y -0.5 10.5 Regresi dengan pangkat 3 -1 11.3 1.35 11.7 2.75 12.62 3 12.88 3.8 13.67 4.2 17.9 5 18.5 6.4 19 n = 9 Pangkat 3 x y -0.5 10.5 0.25 -0.125 0.0625 -0.03125 0.015625 -1 11.3 1 -1 1 -1 1 1.35 11.7 1.8225 2.460375 3.321506 4.4840334375 6.053445 2.75 12.62 7.5625 20.79688 57.19141 157.2763671875 432.51 3 12.88 9 27 81 243 729 3.8 13.67 14.44 54.872 208.5136 792.35168 3010.936 4.2 17.9 17.64 74.088 311.1696 1306.91232 5489.032 5 18.5 25 125 625 3125 15625 6.4 19 40.96 262.144 1677.722 10737.41824 68719.48 Sigma 25 128.07 117.675 565.2363 2964.98 16365.41139063 94013.02 Bentuk Matriks 9 25 117.675 565.2363 25 117.675 565.2363 2964.98 117.675 565.2363 2964.98 16365.41 565.2363 2964.98 16365.41 94013.02 Invers 0.471545 0.135292 -0.13547 0.016479787968 0.135292 0.33236 -0.16296 0.017072467339 -0.13547 -0.16296 0.099988 -0.01145156192 0.01648 0.017072 -0.01145 0.001366566114 Hasil a0 10.10394 a1 -0.4886 a2 0.771647 a3 -0.07334 a0 + a1x + x 2 x 3 x 4 x 5 x 6
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Transcript of turunan 3
Regresixy-0.510.5Regresi dengan pangkat 3-111.31.3511.72.7512.62312.883.813.674.217.9518.56.419n =9Pangkat 3Bentuk Umum : a0 + a1x + a2x^2 + a3x^3
xyx2x3x4x5x6xyx2*yx3*y-0.510.50.25-0.1250.0625-0.031250.015625-5.252.625-1.3125-111.31-11-11-11.311.3-11.31.3511.71.82252.4603753.321506254.48403343756.053445140615.79521.3232528.78638752.7512.627.562520.79687557.19140625157.2763671875432.510009765634.70595.43875262.4565625312.889278124372938.64115.92347.763.813.6714.4454.872208.5136792.351683010.93638451.946197.3948750.100244.217.917.6474.088311.16961306.912325489.03174475.18315.7561326.1752518.52512562531251562592.5462.52312.56.41940.96262.1441677.721610737.4182468719.476736121.6778.244980.736Sigma25128.07117.675565.236252964.980212516365.41139062594013.0239439063413.8162000.49789995.90189
Bentuk Matriks925117.675565.2363a0128.0725117.675565.23632964.98a1413.816117.675565.23632964.9816365.41a22000.498565.23632964.9816365.4194013.02a39995.902Invers 0.47154535160.1352917948-0.13546783440.0164797880.13529179480.3323595161-0.16296233120.0170724673-0.1354678344-0.16296233120.0999881647-0.01145156190.0164797880.0170724673-0.01145156190.0013665661Hasila010.1039363106a1-0.4886015865a20.7716471621a3-0.0733391803Maka didapat persamaan y = 10.10394 - 0.4886x + 0.771647x^2 - 0.07334x^3
Turunan FDA,BDA,CDARumus Turunan Pertama Persamaan Yang Digunakanf(x) = 10.10394 - 0.4886x + 0.771647x^2 - 0.07334x^3f(x) = 10.10394+-0.4886x+0.771647x^2+-0.07334x^3xy-0.510.5Mencari turunan 1, 2 ,3 & 4 dari titik x : -111.3x =2.821.3511.7x =5.852.7512.62< titik 2.82 312.883.813.674.217.9518.5< titik 5.85 6.419n =9TURUNAN PERTAMAx = 2.82x = 5.85keterangan xi+1 = 3f-212.479875099 xi+1 = 6.4f-217.333390125FDA 2 titik = -15.1339567127f0 didapatkan dari f(xi) xi = 2.82f-113.070627625FDA 2 titik = -59.8295935427 xi = 5.85f-117.784615BDA 2 titik = -13.3651313564f1 didapatkan dari f(xi+1) xi-1 = 2.75f013.2178277777BDA 2 titik = -59.396770139 xi-1 = 5f018.97053228CDA 3 titik = 1.4302774182f2 didapatkan dari f(xi+2)h = xi+1 - xi = 0.18f113.602783CDA 3 titik = 1.478209375h = xi+1 - xi = 0.55f119.35792016f-1 didapatkan dari f(xi-1) xi+2 = 3.18f213.9949690599 xi+2 = 6.95f219.360237035FDA 3 titik = 1.05440615f-2 didapatkan dari f(xi-2) xi-2 = 2.46FDA 3 titik = 2.118554464 xi-2 = 4.75BDA 3 titik = -0.0215942182BDA 3 titik = 2.799070873CDA 5 titik = 1.5999385409CDA 5 titik = 1.269513444Maka akan didapat tabel baruxyNilai x baru yang didapat dari tabel :-0.510.5503192512.785-111.43752722.911.3510.67021275535.4252.7513.070627625< titik 2.78546.125titik 2.91 >2.8213.2178277777313.6027833.815.36553024.216.23005916517.784615< titik 5.425titik 6.125 >5.8518.970532286.419.35792016Mencari nilai turunan x baru diantara x x = 2.785x = 2.91
xi+1 = 2.82f-113.070627625 xi+1 = 3f-213.0288637035FDA 2 titik = -135.3887852173 xi = 2.785f-2-46.6286336867FDA 2 titik = 15.5628827392 xi = 2.91f-113.2178277777BDA 2 titik = -133.4555119458 xi-1 = 2.75f013.1440330595BDA 2 titik = 15.475991601 xi-1 = 2.82f013.4092411396CDA 3 titik = 2.138640124h = xi+1 - xi = -5.605f113.2178277777CDA 3 titik = -0.0131311465h = xi+1 - xi = 0.09f113.602783 xi+2 = -8.425f2112.8505642303 xi+2 = 3.09f213.7981325698FDA 3 titik = 2.140422286 xi-2 = 13.995FDA 3 titik = 8.8680956555 xi-2 = 2.73BDA 3 titik = 2.162290108BDA 3 titik = -0.0132005995CDA 5 titik = 2.139234178CDA 5 titik = 2.3535771141x = 5.425titik 6.125
xi+1 = 5.85f-117.784615 xi+1 = 6.4f-218.6553153553FDA 2 titik = -50.488568448 xi = 5.425f-216.9967859178FDA 2 titik = -24.4501510987 xi = 6.125f-118.97053228BDA 2 titik = -49.7759693783 xi-1 = 5f018.4537904359BDA 2 titik = -23.3923625052 xi-1 = 5.85f019.2077843672CDA 3 titik = 0.7043416h = xi+1 - xi = 0.425f118.97053228CDA 3 titik = 1.3951968h = xi+1 - xi = 0.275f119.35792016 xi+2 = 6.275f219.3010605866 xi+2 = 6.675f219.4117882016FDA 3 titik = 0.7209806125 xi-2 = 4.575FDA 3 titik = 1.4349379125 xi-2 = 5.575BDA 3 titik = 0.387555075BDA 3 titik = 1.036529525CDA 5 titik = 0.7098879375CDA 5 titik = 1.4084438375TURUNAN KEDUARumus Turunan Keduaxy-0.510.5-111.31.3511.72.7512.62< titik 2.82312.883.813.674.217.9518.5< titik 5.856.419x = 2.82titk 5.85
xi+1 = 3f-312.1320102691 xi+1 = 6.4f-316.23005916 xi = 2.82f-212.479875099FDA 3 titik = 0.223174 xi = 5.85f-217.333390125FDA 3 titik = -1.272962 xi-1 = 2.75f-113.070627625BDA 3 titik = -13.6898880667 xi-1 = 5f-117.784615BDA 3 titik = 2.4287352231h = xi+1 - xi = 0.18f013.2178277777CDA 3 titik = 7.3381194333h = xi+1 - xi = 0.55f018.97053228CDA 3 titik = -2.6397666116 xi+2 = 3.18f113.602783 xi+2 = 6.95f119.35792016 xi-2 = 2.46f213.9949690599FDA 5 titik = 0.3023812 xi-2 = 4.75f219.360237035FDA 5 titik = -1.03094 xi+3 = 3.36f314.3918196442BDA 5 titik = -34.8763099667 xi+3 = 7.5f318.90427125BDA 5 titik = 7.0131930579 xi-3 = 2.28CDA 5 titik = 9.6833655111 xi-3 = 4.2CDA 5 titik = -3.1760421488Maka akan didapat tabel baruxy-0.510.55031925Nilai x yang didapat dari tabel :-111.43752712.7851.3510.67021275522.912.7513.070627625< titik 2.78535.425titik 2.91 >2.8213.217827777746.125313.6027833.815.36553024.216.23005916517.784615< titik 5.425titik 6.125 >5.8518.970532286.419.35792016Mencari nilai turunan x baru diantara x x = 2.785x = 2.91
xi+1 = 2.82f-312.9250600739FDA 3 titik = 0.3023812 xi+1 = 3f-312.8426697062FDA 3 titik = 0.223174 xi = 2.785f-212.9976303409BDA 3 titik = 0.333184 xi = 2.91f-213.0288637035BDA 3 titik = 0.3023812 xi-1 = 2.75f-113.070627625CDA 3 titik = 0.3177826 xi-1 = 2.82f-113.2178277777CDA 3 titik = 0.2627776h = xi+1 - xi = 0.035f013.1440330595h = xi+1 - xi = 0.09f013.4092411396 xi+2 = 2.855f113.2178277777FDA 5 titik = 0.3177826 xi+2 = 3.09f113.602783FDA 5 titik = 0.2627776 xi-2 = 2.715f213.2919929128BDA 5 titik = 0.3177826 xi-2 = 2.73f213.7981325698BDA 5 titik = 0.2627776 xi+3 = 2.89f313.3665095982CDA 5 titik = 0.3177826 xi+3 = 3.18f313.9949690599CDA 5 titik = 0.2627776 xi-3= 2.68 xi-3= 2.64x = 5.425x = 6.125
xi+1 = 5.85f-316.124083135FDA 3 titik = -1.03094 xi+1 = 6.4f-318.27128505FDA 3 titik = -1.272962 xi = 5.425f-216.9967859178BDA 3 titik = -0.656906 xi = 6.125f-218.6553153553BDA 3 titik = -1.03094 xi-1 = 5f-117.784615CDA 3 titik = -0.843923 xi-1 = 5.85f-118.97053228CDA 3 titik = -1.151951h = xi+1 - xi = 0.425f018.4537904359h = xi+1 - xi = 0.275f019.2077843672 xi+2 = 6.275f118.97053228FDA 5 titik = -0.843923 xi+2 = 6.675f119.35792016FDA 5 titik = -1.151951 xi-2 = 4.575f219.3010605866BDA 5 titik = -0.843923 xi-2 = 5.575f219.4117882016BDA 5 titik = -1.151951 xi+3 = 6.7f319.41159541CDA 5 titik = -0.843923 xi+3 = 6.95f319.360237035CDA 5 titik = -1.151951 xi-3= 4.15 xi-3= 5.3TURUNAN KETIGARumus Turunan Ketigaxy-0.510.5-111.31.3511.72.7512.62< titik 2.82312.883.813.674.217.9518.5< titik 5.856.419x = 2.82x 5.85
xi+1 = 3f-312.1320102691 xi+1 = 6.4f-316.23005916 xi = 2.82f-212.479875099FDA 5 titik = -0.44004 xi = 5.85f-217.333390125FDA 5 titik = -0.44004 xi-1 = 2.75f-113.070627625BDA 5 titik = 117.7023438889 xi-1 = 5f-117.784615BDA 5 titik = -8.3353778813h = xi+1 - xi = 0.18f013.2178277777CDA 5 titik = 38.6473946296h = xi+1 - xi = 0.55f018.97053228CDA 5 titik = -3.3651792938 xi+2 = 3.18f113.602783 xi+2 = 6.95f119.35792016 xi-2 = 2.46f213.9949690599 xi-2 = 4.75f219.360237035 xi+3 = 3.36f314.3918196442 xi+3 = 7.5f318.90427125 xi-3 = 2.28 xi-3 = 4.2Maka akan didapat tabel baruxy-0.510.55031925Nilai x yang didapat dari tabel :-111.43752712.7851.3510.67021275522.912.7513.070627625< titik 2.78535.425titik 2.91 >2.8213.217827777746.125313.6027833.815.36553024.216.23005916517.784615< titik 5.425titik 6.125 >5.8518.970532286.419.35792016
Mencari nilai turunan x baru diantara x x = 2.785x = 2.91
xi+1 = 2.82f-312.9250600739 xi+1 = 3f-312.8426697062 xi = 2.785f-212.9976303409FDA 5 titik = -0.4400400001 xi = 2.91f-213.0288637035FDA 5 titik = -0.44004 xi-1 = 2.75f-113.070627625BDA 5 titik = 0.44004 xi-1 = 2.82f-113.2178277777BDA 5 titik = 0.44004h = xi+1 - xi = 0.035f013.1440330595CDA 5 titik = -0.44004h = xi+1 - xi = 0.09f013.4092411396CDA 5 titik = -0.44004 xi+2 = 2.855f113.2178277777 xi+2 = 3.09f113.602783 xi-2 = 2.715f213.2919929128 xi-2 = 2.73f213.7981325698 xi+3 = 2.89f313.3665095982 xi+3 = 3.18f313.9949690599 xi-3 = 2.68 xi-3 = 2.64x = 5.425x = 6.125
xi+1 = 5.85f-316.124083135 xi+1 = 6.4f-318.27128505 xi = 5.425f-216.9967859178FDA 5 titik = -0.44004 xi = 6.125f-218.6553153553FDA 5 titik = -0.44004 xi-1 = 5f-117.784615BDA 5 titik = 0.44004 xi-1 = 5.85f-118.97053228BDA 5 titik = 0.44004h = xi+1 - xi = 0.425f018.4537904359CDA 5 titik = -0.44004h = xi+1 - xi = 0.275f019.2077843672CDA 5 titik = -0.44004 xi+2 = 6.275f118.97053228 xi+2 = 6.675f119.35792016 xi-2 = 4.575f219.3010605866 xi-2 = 5.575f219.4117882016 xi+3 = 6.7f319.41159541 xi+3 = 6.95f319.360237035 xi-3 = 4.15 xi-3 = 5.3TURUNAN KEEMPATRumus Turunan Keempat
xy-0.510.5-111.31.3511.72.7512.62< titik 2.82312.883.813.674.217.9518.5< titik 5.856.419x = 2.82x = 5.85f-411.80164153f-415.03450381 xi+1 = 3f-312.1320102691 xi+1 = 6.4f-316.23005916 xi = 2.82f-212.479875099FDA 5 titik = -2847.4383758573 xi = 5.85f-217.333390125FDA 5 titik = -31.4984751315 xi-1 = 2.75f-113.070627625BDA 5 titik = -868.6096584362 xi-1 = 5f-117.784615BDA 5 titik = 21.2737403183h = xi+1 - xi = 0.18f013.2178277777CDA 5 titik = -868.6096584362h = xi+1 - xi = 0.55f018.97053228CDA 5 titik = 21.2737403183 xi+2 = 3.18f113.602783 xi+2 = 6.95f119.35792016 xi-2 = 2.46f213.9949690599 xi-2 = 4.75f219.360237035 xi+3 = 3.36f314.3918196442 xi+3 = 7.5f318.90427125 xi-3 = 2.28f411.80164153 xi-3 = 4.2f415.03450381 xi+4 = 3.54 xi+4 = 8.05 xi-4= 2.1 xi-4= 3.65Maka akan didapat tabel baruxy-0.510.55031925Nilai x yang didapat dari tabel :-111.43752712.7851.3510.67021275522.912.7513.070627625< titik 2.78535.425titik 2.91 >2.8213.217827777746.125313.6027833.815.36553024.216.23005916517.784615< titik 5.425titik 6.125 >5.8518.970532286.419.35792016
Mencari nilai turunan x baru diantara x x = 2.785x = 2.91f-412.8529356908f-412.659566575 xi+1 = 2.82f-312.9250600739 xi+1 = 3f-312.8426697062 xi = 2.785f-212.9976303409FDA 5 titik = -392118.801446067 xi = 2.91f-213.0288637035FDA 5 titik = -23371.5151056242 xi-1 = 2.75f-113.070627625BDA 5 titik = -0.0000000024 xi-1 = 2.82f-113.2178277777BDA 5 titik = 0.0000000001h = xi+1 - xi = 0.035f013.1440330595CDA 5 titik = -0.0000000107h = xi+1 - xi = 0.09f013.4092411396CDA 5 titik = 0.0000000001 xi+2 = 2.855f113.2178277777 xi+2 = 3.09f113.602783 xi-2 = 2.715f213.2919929128 xi-2 = 2.73f213.7981325698 xi+3 = 2.89f313.3665095982 xi+3 = 3.18f313.9949690599 xi-3 = 2.68f412.8529356908 xi-3 = 2.64f412.659566575 xi+4 = 2.925 xi+4 = 3.27 xi-4= 2.645 xi-4= 2.55x = 5.425x = 6.125f-415.2002865972f-417.8275928209 xi+1 = 5.85f-316.124083135 xi+1 = 6.4f-318.27128505 xi = 5.425f-216.9967859178FDA 5 titik = -124.6903141869 xi = 6.125f-218.6553153553FDA 5 titik = -238.9384126221 xi-1 = 5f-117.784615BDA 5 titik = -0 xi-1 = 5.85f-118.97053228BDA 5 titik = -0h = xi+1 - xi = 0.425f018.4537904359CDA 5 titik = -0h = xi+1 - xi = 0.275f019.2077843672CDA 5 titik = -0 xi+2 = 6.275f118.97053228 xi+2 = 6.675f119.35792016 xi-2 = 4.575f219.3010605866 xi-2 = 5.575f219.4117882016 xi+3 = 6.7f319.41159541 xi+3 = 6.95f319.360237035 xi-3 = 4.15f415.2002865972 xi-3 = 5.3f417.8275928209 xi+4 = 7.125 xi+4 = 7.225 xi-4= 3.725 xi-4= 5.025maka turunan :f(x)10.10394+-0.4886x+0.771647x^2+-0.07334x^3f'(x)-0.4886+1.543294x+-0.22002x^2f''(x)1.543294+-0.44004xf'''(x)-0.44004f''''(x)0
Sheet3
