Help with Calc please!

Question

Below is the graph of f '(x), the derivative of f(x), and has x-intercepts at x = -3, x = 1, and x = 2 and a relative maximum at x = -1.5 and a relative minimum at x = 1.5. Which of the following statement is true?

Options:

1)	f is concave up from x = 0 to x = 3.
2)	f has an inflection point at x = 0.
3)	f is concave down from x = -1.5 to x = 1.5.
4)	None of these is true.

Answer 1

If the graph of the derivative of a function f'(x) is decreasing, that means the original graph for f(x) is concave down. Since the graph of f'(x) is decreasing between -1.5 and 1.5, f(x) must be concave down. Hence, Option 3) is correct.