$\begingroup$

I started by taking the first order partial derivatives:

$F_{x}=-3x^{2}+2y + 1$

$F_{y}=-2y+2x $

$F_{z}=2 $

Now I would try to solve it for $F_{x}=F_{y}=F_{z}=0$ but $F_{z}=2$. How can I proceed or this means that $F$ doesn't have critical points?

$\endgroup$ 2

1 Answer

$\begingroup$

You are correct that there are no critical points, because $F_z = 2 \neq 0$: there are no points $(x, y, z)$ at which the partial derivatives are simultaneously $0$.

$\endgroup$ 0

Your Answer

Sign up or log in

Sign up using Google Sign up using Facebook Sign up using Email and Password Submit

Post as a guest

Post Your Answer Discard

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