anonymous
  • anonymous
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)
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[f(x,y)=x^2+y^2+x^2y+4 \] \[D=\left| x \right|\le 1, \left| y \right|\le 1\]
anonymous
  • anonymous
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
anonymous
  • anonymous
when u want to find max and min at boundaries for example this one|dw:1349636466076:dw|

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anonymous
  • anonymous
\(x=1\) 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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