# To find Max/Min on a closed function

• Apr 24th 2009, 09:08 AM
fearless901
To find Max/Min on a closed function
Find local Max/Min of the function z=f(x,y) = (2x-x^2)(2y-y^2) by finding the critical points of F and then classifying each critical point as to whether it is a local max or local min or saddle point.
• Apr 24th 2009, 11:57 AM
Calculus26
Is your question about the general method or this problem in particular?

If it is generally how do you find and classify local extrema see attachment where I have answered a similar question
• Apr 26th 2009, 09:29 PM
fearless901
to find local max/min z=f(x,y)= (2x-x^2)(2y-y^2)
do I multiply the function first??
or just the the partial diff as it is?
• Apr 26th 2009, 09:44 PM
redsoxfan325
Quote:

Originally Posted by fearless901
to find local max/min \$\displaystyle z=f(x,y)= (2x-x^2)(2y-y^2)\$
do I multiply the function first??
or just the the partial diff as it is?

You'll get the same answer either way. Do what's easiest. I'd recommend taking as is, because when you take the partial w.r.t \$\displaystyle x\$, \$\displaystyle (2y-y^2)\$ is a constant and vice versa.