calculus question

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.

Answer 1

Hello,

All the statements appear to be True.

1)Inflection point exists between the region as the curve goes from concave down to concave up

2)the derivative (slope) is increasing implying that the function is increasing.

3) It is a relative maximum at that point as it reaches a tangent(slope =0 for f'(x)) and starts to fall down with increasing x value.