Hello
Im trying to find all the critical points of this functions.
Could somebody please give me a hand?
Thanks Heaps
Hello,
$\displaystyle f(x,y)=x^2+x^2y+5y^2+2y^3$
$\displaystyle \frac{\partial f}{\partial x} (x,y)=2x+2xy=2x(1+y)$
$\displaystyle \frac{\partial f}{\partial y} (x,y)=x^2+10y+6y^2$
You have to solve simultaneously these equations :
$\displaystyle \left\{ \begin{array}{ll} 0&=2x(1+y) \\ 0&=x^2+10y+6y^2 \end{array} \right.$
from the first equation, you know that either x=0, either y=-1.
Then substitute in the second equation, for each possible value.
Then, calculate the Hessian matrix, and here, I don't know how much you've learnt :/
Sorry, I didn't see your answer...
Take a look at this link : Hessian matrix - Wikipedia, the free encyclopedia
Normally, everything is explained (Note that you have to take the values of the second derivatives at the critical points).
I don't feel like typing all the tex, but I can do it by hand if you really need it