Question

If the graph of f " (x) is continuous and has a relative maximum at x = c, which of the following must be true?

A. The graph of f has a relative maximum at x = c.
B. The graph of f has an inflection point at x = c.
C. The graph of f has a relative minimum at x = c.
D. None of the above is necessarily true.

Answer 1

The relative extrema of a second derivative don't tell you anything about f(x)'s extrema of inflection points

Answer 2

are you suggesting the answer is D?

Answer 3

I think so, since zeros of f ' (x) give relative extrema of f(x) and zeros of f " (x) give inflection points.

Answer 4

yep it was right thank you