Help me check my calculus

Question

1. 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.

I chose B. Is it correct?

Answer 1

Yes, the slope is always positive, goes up forever.