1. ## Derivatives

Problem
Given $\displaystyle f\left( x,y \right)=e^{2x^{2}+4xy^{2}-x}$,
find and classify the extremes.

Attempt
I have a problem with the second derivatives. That expression would be huge. Have I been thinking wrong? Here's my calculations:
* 2012-09-07 15.15.06.jpg
* 2012-09-07 15.15.15.jpg
* 2012-09-07 15.15.21.jpg

The method I use to classify is:
When $\displaystyle A\mbox{C}-B^{2}$ is positive, we have a min or maximum. If A>0 then it's a min, if A<0 it's a maximum. If $\displaystyle A\mbox{C}-B^{2}$ is negative, then we have a saddle point.
$\displaystyle \left(A=\frac{\partial ^{2}}{\partial x^{2}},\; B=\frac{\partial ^{2}}{\partial xy},\; \mbox{C}=\frac{\partial ^{2}}{\partial y^{2}} \right)$

2. ## Re: Derivatives

You're doing it correctly, including the classification. You just need to keep going. For A, where you stopped for some reason, plug f and df/dx in and you're done. (Actually, you don't even need to do that much work, since you're evaluating it at 3 points (0,.5), (0,-.5), (.25,0) where you already know df/dx=0. Thus A(P)=4f(P) when P is one of those 3 points.)

3. ## Re: Derivatives

The second derivatives are NOT 'huge'. They are not a problem if you are careful.

thanks