Second Derivative and Concavity

Question

Which of the following statements correctly describes the relationship between the second derivative of a function and its concavity?

Accepted Answer

If $$f''(x) > 0$$ on an interval, then the function is concave up on that interval.

Answer

If $$f''(x) > 0$$ on an interval, then the function is concave down on that interval.

Answer

If $$f''(x) < 0$$ on an interval, then the function is always increasing on that interval.

Answer

If $$f''(x) = 0$$ on an interval, then the function has an absolute maximum on that interval.

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