Question

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.

Answer 1

im thinking D

Answer 2

any hints ?

Answer 3

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.

Answer 4

well i know wherever f''(x) is positive f(x) is concave up and vice versa

Answer 5

but i don't know much about what maxima and minima mean in the second derivative

Answer 6

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

Answer 7

thank you

Answer 8

No worries. Best of luck^^