0
$\begingroup$

Determine local max., local min., and saddle points of the following function: $4x + 4y + x^2y + xy^2$

I know that we take the gradient vector and set it equal to zero to find the critical points. And observe the behavior of the determinant to decide whether a point is a saddle point,local max, or local min.

The gradient that I found was:$<4+2xy+y^2, 4+x^2+2xy>$. When I set them equal to zero, I'm unable to solve the system of equations.

Any help is appreciated.

$\endgroup$
  • 1
    $\begingroup$ Try subtracting them. $\endgroup$ – quasi Nov 1 '17 at 19:22
0
$\begingroup$

you have $$4+2xy=-y^2$$ and $$4+2xy=-x^2$$ therefore $$-x^2=-y^2$$ or $$(x-y)(x+y)=0$$

$\endgroup$
  • $\begingroup$ This will evaluate to: x = y, x = -y. So we just plug in random numbers to get the critical points? $\endgroup$ – Bharat Edupghanti Nov 1 '17 at 21:34

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.