I'm having much more trouble with this than i should. 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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I'm having much more trouble with this than i should. 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.

Mathematics
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im thinking D
any hints ?
First of all, do you know the definition of the second derivative. If you have a function f(x) and take the second derivative f''(x). What does that say? Hope that leads you somewhere.

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well i know wherever f''(x) is positive f(x) is concave up and vice versa
but i don't know much about what maxima and minima mean in the second derivative
The second derivative tells you whether or not your point on f(x) is a local maximun or minimum. You can find, I think your answer here. https://en.wikipedia.org/wiki/Second_derivative_test
thank you
No worries. Best of luck^^

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