I am working with the function:
$f(x) = 4x^5 - 3x^4 + 2x^3 - x^2 + 3$.
One of the critical points $f'(x) = 0$ occurs when $x=0$. Checking the second derivative, we see that $f''(0) = -2$. This would lead one to the conclusion that the point $x=0$ is a local maximum.
So, I am just wondering how we could conclude it is a saddle point if the second derivative is (incorrectly?) saying it is a local max.