## jwcox118 2 years ago 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)<or=1, abs(y)<or=1

1. jwcox118

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

2. mukushla

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

3. mukushla

when u want to find max and min at boundaries for example this one|dw:1349636466076:dw|

4. mukushla

$$x=1$$ and $$-1\le y \le1$$ ... ur function will be$f(x,y)=f(1,y)=y^2+y+5$which is a one variable function with respect to y and u can max and min of it easily :)