# Extrema for Single Variable Functions (2nd Deriv Test)

Using the 2nd derivative test, we know that if the value from evaluating critical points at the 2nd derivative is greater than 0, then it is a local min. If the value is less than 0, then it is a local max.

However, if the value is = 0, then it is "inconclusive".

What does this mean? Is it considered an inflection point/saddle point?

Careful: $f''(c) > 0$ implies local min, not max.
It may not be an inflection point; this all depends on the particular function. It is indeed inconclusive. Consider $f(x) = x^4$. Clearly $x=0$ is critical, but $f''(0)=0$. But still, $x=0$ clearly gives a local min and is not an inflection point. The function $f(x)=x^3$ shows that the critical point may be an inflection point.