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?

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?

Graph of a function that increases from negative infinity to x equals negative 1.5, decreases from x equals negative 1.5 to x equals 1.5, crossing the y axis at y equals 6, and increases from x equals 1.5 to positive infinity with x intercepts at x equals negative 3, 1 and 2.

A	f has a relative minimum at x = 1.5.
B	f has a relative maximum at x = -1.5.
C	f is decreasing on the interval from x = 1 to x = 2.
D	None of these is true.

Answer 1

A. "f has a relative minimum at 1.5"

False.

f can have a relative minimum only where f' is 0.

B. "f has a relative maximum at -1.5"

False.

f can have a relative maximum only where f' is 0.

C. "f is decreasing on the interval from x = 1 to x = 2".

True.

f is decreasing where f' is negative.