### Home > APCALC > Chapter 5 > Lesson 5.2.2 > Problem5-70

5-70.

Ima Geek is announcing her mystery function contest again. Today’s mystery function has these properties: $f^{\prime\prime}(–3) = f^\prime(–3) = f (–3) = 0$. What do you know about the graph? What don’t you know? Homework Help ✎

When a 1st-derivative is equal to zero at $x = a$, then $x = a$ is a CANDIDATE for a local max or a local min. When a 2nd-derivative is equal to zero at $x = a$, then $x = a$ is also a CANDIDATE for a point of inflection. Obviously, the candidate cannot hold all three positions... so, how do we determine if $x = a$ is a local max, a local min or a POI?