# Wile e coyote looks down and realizes he is walking

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Question 6.(12 points) Wile E. Coyote looks down and realizes he is walking on asheet of ice with thickness given by the functionT(x, y) =x2y-sin(y).a. (8 points) If Mr. Coyote starts at the point(3, π)and walks towards the point(0, π), find the rate of change of thickness of the ice in the direction he travels.
b. (4 points) In which direction should Mr. Coyote go if he wants to maximizethe rate at which the thickness increases?
Math 230 Test 2, SolutionsFall Quarter 2013Page 8 of 9Question 7.(10 points) Letg(x, y)be a differentiable function. Suppose thatxandyare functions of the variablessandtgiven byx(s, t) = 4s3-st2andy(s, t) = 3t-s2.Use the following table to compute the partial derivative∂g∂t(s,t)=(-1,2)(x, y)g(x, y)gx(x, y)gy(x, y)(0,5)6-35(-1,2)-1469
Math 230 Test 2, SolutionsFall Quarter 2013Page 9 of 9