Let f(x) be a polynomial function such that f(4)=-1, f’(4)=2 and f”(4)=0. If x<4, then f”(x)<0 and if x>4, then f”(x)>0. The point (-4, -1) is which of the following for the graph of f?

Question

A. relative maximum
B. relative minimum
C. critical value
D. inflection point
E. none of these

I'm confused on how to figure this out. Thanks for your time and help.

Answer 1

Since we know nothing about f'(-4) or f"(-4), we can say nothing about the properties of f there.

However, if the change in sign is inadvertent, and all the data are about x=4,

since f"(4)=0, x=4 is an inflection point.