Answer true or false. If f '(x) 0 for all x on the interval I, then f(x) is concave up on the interval I.

Question

Answer true or false. If f '(x) > 0 for all x on the interval I, then f(x) is concave up on the interval I.

Quizplus · Accepted Answer

The condition given in the statement is that the first derivative of f(x) is always greater than zero on the interval I. This only tells us that f(x) is increasing on that interval, but it does not necessarily imply that the second derivative (which determines the concavity) is positive. Therefore, f(x) may or may not be concave up on the interval I.

Answer True or False