I have a region x^2 + y^2 <= 1 and y>=0. It's temperature function is f(x,y) x^2 - 2y^2 + x + y. How do I find the max and min temperatures on the lower boundary y=0?
I took the derivatives with respect to x and with respect to y such that:
fx:=diff(f(x,y),x);
fy:=diff(f(x,y),x);
Then I used fsolve({fx=0, fy=0},{x,y}) which game me (-0.5, 0.25)
Is there really only one critical point on that lower bound...