Question

If the graph of f '(x) has an X-intercept at x = C, which of the following must be true?

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

Answer 1

None of the above is true

Answer 2

Answer: D

Step-by-step explanation:

f'(C) = 0 ⇒ There is a critical point here

There could be a relative max or min here, but since we do not know if f''(x) is positive or negative, we cannot be sure if the function is truly changing from positive to negative or vice versa. "C" could simply be at a horizontal tangent of a function like x³.