# HW09-solutions - walker (nw4695) HW09 schultz (53990) This...

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walker (nw4695) – HW09 – schultz – (53990)1Thisprint-outshouldhave20questions.Multiple-choice questions may continue onthe next column or page – find all choicesbefore answering.00110.0pointsFrom the contour map offshown belowdecide whetherfx, fyare positive, negative,or zero atP.00-2-2-4-4-6-6Pxy1.fx>0,fy<02.fx<0,fy<0correct3.fx<0,fy>04.fx<0,fy= 05.fx>0,fy>06.fx>0,fy= 0Explanation:When we walk in thex-direction fromPweare walking downhill, sofx<0. On the otherhand, when we walk in they-direction fromPwe are again walking downhill, sofy<0 also.Consequently, atPfx<0,fy<0.keywords: contour map, slope, partial deriva-tive,00210.0pointsDeterminefxwhenf(x , y) = (x2+ 2y)(y2-x).1.fx= 2xy2+ 2y-3x22.fx= 4xy2-y+ 3x23.fx= 2y-2xy2-3x24.fx=y-4xy2+ 3x25.fx= 2xy2-2y-3x2correct6.fx=y+ 4xy2+ 3x2Explanation:From the Product Rule we see thatfx= 2x(y2-x)-(x2+ 2y).Consequently,fx= 2xy2-2y-3x2.00310.0pointsDeterminefywhenf(x, y) = sin(x-y)-ycos(x-y).1.fy=-2 cos(x-y)-ysin(x-y)correct2.fy=ycos(x-y)3.fy=ysin(x-y)4.fy=-ycos(x-y)5.fy=-2 sin(x-y) +ycos(x-y)6.fy=-ysin(x-y)7.fy= 2 sin(x-y)-ycos(x-y)
walker (nw4695) – HW09 – schultz – (53990)28.fy= 2 cos(x-y) +ysin(x-y)fx= 8y+x2,fy= 6x+ 2xy00410.0pointsFind the slope in thex-direction at thepointP(0,2, f(0,2)) on the graph offwhen2.fx= 8y+x2,fy= 6x+ 2xy
f(x, y) = 3(2x+y)e-xy.1.slope =-142.slope =-123.slope =-104.slope =-85.slope =-6On the other hand,differentiatingf(x, y)with respect toyholdingxfixed, we see thatfy= 8y+x2.00610.0pointsFind the value offxat (2,2) whenf(x, y) = 4x3-8x2y-8x+ 3y.

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