
Max/Min with constraint
I need help on the following problem:
Find the absolute maximum and minimum of the function $\displaystyle f(x,y) = x^2 + y^2 $ subject to the constraint $\displaystyle x^4 + y^4 = 625 $.
I tried using Lagrange's multiplier to this problem but here is where I'm stuck.
$\displaystyle \frac{\partial f}{\partial x}= \lambda\frac{\partial g}{\partial x}$
$\displaystyle 2x = 4x^3 \lambda $
$\displaystyle \frac{\partial f}{\partial y} = \lambda\frac{\partial g}{\partial y}$
$\displaystyle 2y = 4y^3\lambda $
I just can't seem to be able to solve for $\displaystyle x,y, \lambda $,which I need for the critical points

Where is your third equation?
$\displaystyle 2x\;=\;4x^{3}\lambda$
$\displaystyle 2y\;=\;4y^{3}\lambda$
$\displaystyle x^{4}\;+\;y^{4}\;=\;625$
That should do it.