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?
A. f is concave down from x = –3 to x = 0.
B. f is decreasing from x = –1.5 to x = 1.5.
C. f has a relative maximum at x = 1.
D. None of these is true.

Answer 1

Answer:

C. f has a relative maximum at x = 1.

Step-by-step explanation:

A. False.  f(x) is concave down when f"(x) is negative.  f"(x) is the tangent slope of the graph, f'(x).  So f(x) is concave down between x = -1.5 and x = 1.5.

B. False.  f(x) is decreasing when f'(x) is negative.  So f(x) is decreasing in the intervals x < -3 and 1 < x < 2.

C. True.  f(x) has a relative maximum where f'(x) = 0 and changes from + to -.