Question

Find the absolute maximum and minimum values of f on the set D.
f(x,y) = x^2+y^2+(x^2)y+4
D = abs(x) 13 years ago

Answer 1

\[f(x,y)=x^2+y^2+x^2y+4 \]
\[D=\left| x \right|\le 1, \left| y \right|\le 1\]

Answer 2

ok u have a continous function so u just need to find extremums in given region ; setting partial derivatives equal to zero\[\frac{\partial f}{\partial x}=0\]\[\frac{\partial f}{\partial y}=0\]and finally compare the values of extremums with value of function at boudaries

Answer 3

when u want to find max and min at boundaries for example this one