"Let f(x,y)=2(x^2)y-(y^3)+x-4.

Question

a) Find the local linearization of f at (3,1)

b) Compute the directional derivative of f at (3,1) in the direction towards the point (-2,3). At (3,1), is the function f increasing or decreasing in the direction towards the point (-2,3)? Give a reason for your answer.

c) What direction, given as a unit vector, gives the maximum instantaneous rate of change in the function at (3,1)? In what direction, given as a unit vector, is the instantaneous rate of change at (3,1) equal to 0?"

Thanks for your help!