### Home > CALC > Chapter 5 > Lesson 5.2.2 > Problem 5-70

5-70.

Today's mystery function has these properties: *f* ″(−3) = *f* ′(*−*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?