trevino ochoa (dt23653) – HW09 – mostovyi – (54020)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= 03.fx<0,fy>04.fx>0,fy>05.fx<0,fy<06.fx<0,fy= 0correctExplanation:When we walk in thex-direction fromPweare walking downhill, sofx<0. On the otherhand, when we walk in they-direction fromPour elevation doesn’t change because we arewalking along a contour, sofy= 0.Consequently, atPfx<0,fy= 0.keywords: contour map, slope, partial deriva-tive,00210.0pointsDeterminefxwhenf(x , y) = (x2+y)(2y2-x).1.fx=y-4xy2-3x22.fx= 2y-2xy2+ 3x23.fx= 4xy2+y-3x24.fx= 2xy2-2y+ 3x25.fx= 2y+ 2xy2+ 3x26.fx= 4xy2-y-3x2correctExplanation:From the Product Rule we see thatfx= 2x(2y2-x)-(x2+y).Consequently,fx= 4xy2-y-3x2.00310.0pointsDeterminefywhenf(x, y) = sin(4x-y)-ycos(4x-y).1.fy=-2 cos(4x-y)-ysin(4x-y)correct2.fy=ycos(4x-y)3.fy= 2 sin(4x-y)-ycos(4x-y)4.fy= 2 cos(4x-y) +ysin(4x-y)5.fy=ysin(4x-y)6.fy=-ycos(4x-y)