Hey i'm having difficulty solving this problem:
Find the absolute maximum and minimum values of f on the set D.
f(x, y) = xy2 + 7 D = {(x, y) | x ≥ 0, y ≥ 0, x2 + y2 ≤ 3}
I tried doing this:
fx = y^2
fy = 2xy
critical point: (0,0)
then i got $\displaystyle y^2 = 3-x^2$ and plugging that in to the original to get $\displaystyle g(x) = f(x,y) = -x^3+3x+7$. setting that equal to zero i get x=1,-1. but i'm totally lost on what to do from here (or even if i've started correctly). Any and all help is greatly appreciated.
Thanks.