Answer:
absolute maximum is f(1, 0) = 2 and the absolute minimum is f(−1, 0) = −2.
Step-by-step explanation:
We compute,
Hence, if and only if (x,y) = (0,0)
This is unique critical point of D. The boundary equation is given by
Hence, the top half of the boundary is,
On T we have,
We compute
0 if and only if x=0, x= 1/2 or x = -2.
We disregard
Hence, the critical points on T are (0,1) and
On the bottom half, B, we have
Therefore, the critical points on B are (0,-1) and
It remains to evaluate f(x, y) at the points .
We should consider latter two points, , since they are the boundary points for the T and also B. We compute
We conclude that the absolute maximum = f(1, 0) = 2
And the absolute minimum = f(−1, 0) = −2.