Question: Problem 8. The temperature at a point in the plane is T(x,y)=100-4x3-3y2. A bug is at the point (-1,1).(a) Compute gradT(-1,1).(b) Find the rate of

Problem 8. The temperature at a point in the plane is T(x,y)=100-4x3-3y2. A bug is at the point (-1,1).(a) Compute gradT(-1,1).(b) Find the rate of change of temperature in the direction of vec(v)=(3,4).(c) Find the direction in which the bug should move to increase its temperature the fastest.(d) What is the maximum rate of increase of temperature?(e) Find a direction in which the bug should move to NOT change its temperature.

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