# Max/Min with constraint

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• November 14th 2009, 01:05 PM
storchfire1X
Max/Min with constraint
I need help on the following problem:

Find the absolute maximum and minimum of the function $f(x,y) = x^2 + y^2$ subject to the constraint $x^4 + y^4 = 625$.

I tried using Lagrange's multiplier to this problem but here is where I'm stuck.

$\frac{\partial f}{\partial x}= \lambda\frac{\partial g}{\partial x}$

$2x = 4x^3 \lambda$

$\frac{\partial f}{\partial y} = \lambda\frac{\partial g}{\partial y}$

$2y = 4y^3\lambda$

I just can't seem to be able to solve for $x,y, \lambda$,which I need for the critical points
• November 14th 2009, 04:04 PM
TKHunny
Where is your third equation?

$2x\;=\;4x^{3}\lambda$

$2y\;=\;4y^{3}\lambda$

$x^{4}\;+\;y^{4}\;=\;625$

That should do it.