# The Second Derivative Test ![[Function (in Algebra)#^g14unt]] **To determine if a critical point is a local maximum or a local minimum, you can look at the value of the second derivative at $x$. If $f''(x) > 0$, the critical point is a local minimum, and if $f''(x) < 0$, the point is a local maximum.** Note the edge case, **when $f''(x) = 0$**, in which case **the second derivative test cannot be used to distinguish between a local maximum and a local minimum.** In this case the critical point is probably neither, such as with $x^3$ at $x=0$. These points are called *inflection points*. ![[Function (in Algebra)#^xi1i4g]]