Find the absolute maximum and minimum values of f on the set D. f(x, y)=2x^3+y^4, D={(x, y) | x^2+y^2<=1}.

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.

only 10/60 isn't equivalent

hope this : )