Question: The graph of f ′ (x) is continuous, positive, and ... The graph of f ′ (x) is continuous, positive, and has a relative maximum at x = 0. Which of the following statements must be true?

A. The graph of f is always concave down.

B. The graph of f is always increasing.

C. The graph of f has a relative maximum at x = 0.

D. The graph of f has a relative minimum at x = 0.

Question

Mathematics

Franco Guerrero

2 May, 14:28

Question: The graph of f ′ (x) is continuous, positive, and ... The graph of f ′ (x) is continuous, positive, and has a relative maximum at x = 0. Which of the following statements must be true?

A. The graph of f is always concave down.

B. The graph of f is always increasing.

C. The graph of f has a relative maximum at x = 0.

D. The graph of f has a relative minimum at x = 0.

+2

Answers (1)

Know the Answer?

Tony Duncan · Answer 1

If the graph f' (x) is continuous, positive ... means that the slope of the graph is always positive, which in turn means that the graph is always increasing.

Recall that a graph is increasing when it has a positive slope (f' (x) >0) and

decreasing when it has a negative slope (f' (x) <0)