Examine the function f(x,y) = y2 + 4xy + 3x2 + x3 for extreme values.

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written 3.0 years ago by

teamques10 ★ 65k

modified 2.5 years ago by

binitamayekar ★ 6.4k

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written 3.0 years ago by

teamques10 ★ 65k

We have, $f(x,y)=y^2 + 4xy + 3x^2 + x^3$

Step I:

$f_x = 4y+6x+3x^2$

$f_y = 2y+4x$

$f_{xx} = 6 + 6x$

$f_{xy} = 4$

$f_{yy}=2$

Step II:

We now solve $f_x = 0, \ f_y=0$ simultaneously,

$4y+6x+3x^2 = 0 $ and $2y+4x=0$

Putting $2y=-4x$ in first equation

$3x^2 - …

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