Answer true or false. If f '(x)

Name: Answer true or false. If f '(x) < 0 for all x on the interval I, then f(x) is concave down on the interval I.
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Question

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

Quizplus · Accepted Answer

The statement is false. If f F1F1F1S1F1F1F10(x) < 0 for all x on the interval I, it only tells us that the derivative of f is strictly decreasing on the interval I. It does not necessarily imply that f(x) is concave down on the interval I. Concavity depends on the second derivative of f, which can be positive, negative, or zero.

Answer True or False