finding absolute maxima and minima

[yam]

find the maximum value of f(x,y) = x^(2)*y*e^(-x) in the domain 0<x<4 and 0<y<4

 

[blamocur]

I could not understand your writing, but your max value of [imath]64e^{-4} \approx 1.7222[/imath] is not correct. Even at point (3,3) the function value [imath]27e^-3 \approx 1.344[/imath] is higher.
BTW, the domain defined in the problem does not include the borders, so the (4,4) point could not be a solution. Did you, by chance, mean [imath]0\leq x \leq 4, 0\leq y \leq 4[/imath]?