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Question: Finding maximum and minimum values

Question:Finding maximum and minimum values

Red Horse 10 Maple
February 12 2012
0

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 y=0? I must be doing something wrong here.

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