5. (15 pts.) Calculate the first and second partial derivatives of the function
1. (25 pts.) Find the critical points of the function
and determine which of rel max, rel min, or saddle point, each is.
2. (20 pts.) Find the maximum value of the function
subject to the constraint g(x,y) = x2+2y2 = 5 .
5. Evaluate the following double integrals (10 pts. each):
(a): ò01 ò12 x2y-y2x dx dy
(b): ò01 òÖx1 xÖy dy dx
5. (20 pts.) Evaluate the integral
by changing the order of integration. (Trust me, you can't evaluate it in the order in which it is given!)
2. (20 pts.) Find the local extrema of the function
and determine, for each, if it is a local max. local min, or saddle point.
3. (20 pts.) Find the maximum and minimum values of the function
subject to the constraint
4. (20 pts.) Evaluate the interated integral
by rewriting the integral to reverse the order of integration.
(Note: the integral cannot be evaluated in the order given....)