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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.

Respuesta :

mathmate
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)

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