I really need help with math homework. Please and thank you!

Question

If the graph of f '(x) is continuous and decreasing with an x-intercept at x = c, which of the following must be true?

Options:

1)	The graph of f has a relative maximum at x = c.
2)	The graph of f has an inflection point at x = c.
3)	The graph of f has a relative minimum at x = c.
4)	None of the above is necessarily true.

Answer 1

What you really need to do is study and understand what information f'(x) is giving you about f(x). In particular, f(x) is increasing when f'(x) > 0, f(x) is decreasing when f'(x) < 0, and f(x) has a horizontal tangent line when f'(x) = 0. If you take a few minutes to reflect on the ramifications of these statements to the problem at hand, the answer will be obvious to you.