# Thread: Help with max/min with 2 variables

1. ## Help with max/min with 2 variables

f = x^4 + y^4 - 4xy

I know how to find the critical points and test whether they are local min or max. However, for the function above, I found many critical points that could all be classified as local minimum.

The answer only gives two of those points as local minimum.

Can anyone suggest what I do after i find many critical points that could all be local minimum?

2. Just one question:
how was the function given: like f(x) = ;or y= ;or like what you posted?

3. the function was given as f(x,y) =

4. Originally Posted by messianic
f = x^4 + y^4 - 4xy

I know how to find the critical points and test whether they are local min or max. However, for the function above, I found many critical points that could all be classified as local minimum.

The answer only gives two of those points as local minimum.

Can anyone suggest what I do after i find many critical points that could all be local minimum?
There are three critical points, found by solving $x^3 - y = 0$ and $y^3 - x = 0$ simultaneously:

(0, 0), (1, 1) and (-1, -1).

Their nature is tested in the usual way.

If you need more help, please post all your work and say where you're stuck.