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 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
 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

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jwcox118
 2 years ago
Best ResponseYou've already chosen the best response.0\[f(x,y)=x^2+y^2+x^2y+4 \] \[D=\left x \right\le 1, \left y \right\le 1\]

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1ok 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

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1when u want to find max and min at boundaries for example this onedw:1349636466076:dw

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1\(x=1\) 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 :)
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