Would it be possible to answer this question Thank you Suppo

Would it be possible to answer this question? Thank you

Suppose the temperature T is given by T = x3 + y3 - 3xy. Find and classify all critical points of T. Find the hottest point on the square plate bounded by x = 0,x = 2 and y = 0,3/ = 3.

Solution

fx(x,y)=3x^2-3y fy(x,y)=3y^2-3x for finding the critical points fx(x,y)=0=fy(x,y) (a)so critical points are (0,0) and (1,1) (b) hottest point on the plate is (0,0)