Question

Find the local and absolute extrema of the function

f(x,y)=y³+3x²y-6x²-6y²+2 on [-3,3]x[-1,5]

Find the absolute and relative maxima and minima if they exist. Proceed as follow

Compute the first-order partial derivatives
Find the critical points
Compute the second-order partial derivatives
Use the second derivatives test to classify the critical points
Find the value of the function at the local extrema if they exist
Find the absolute maxima and minimum by evaluation f on the boundary of D