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.
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The relative extrema of a second derivative don't tell you anything about f(x)'s extrema of inflection points
are you suggesting the answer is D?
I think so, since zeros of f ' (x) give relative extrema of f(x) and zeros of f " (x) give inflection points.