Calculus graph included need help under standing all the problem is included

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. There are horizontal tangents at x = –1.5 and x = 1.5. Which of the following statements is true?

f has an inflection point in the interval x = –1 to x = 1.

f is increasing on the interval from x = –3 to x = 1.

f has a relative maximum at x = –1.5.

None of these is true.

are none of these true?

Answer 1

Between x= -1 and x=1 f'(x) does not have an inflection point because f'(x)'s slope does not change signs.

Since f'(x) =0 at x=-3, 1, 2 extrema could only occur at those critical points.

There can't be a maximum at x =-1.5

From your description I gather that f'(x) >0 between x=-3 and x=1 therefore f(x) must be increasing during that same interval.

f is increasing on the interval from x = –3 to x = 1. is the correct answer