Question

assume the function f is differentiable over the interval (-∞,∞). classify the following statement as either true or false. if the statement is false, explain why. a function f can have no extrema but still have at least one point of inflection. select the correct choice below. a. the statement is true. b. the statement is false. if a function has a point of inflection it must have at least one extrema. c. the statement is false. all functions have at least one extrema and one point of inflection. d. the statement is false. if a function has no extrema, it cannot have a point of inflection.

Explanation:

Step1: Recall definitions

A point of inflection is a point where the concavity of a function changes. An extrema is a maximum or minimum point. A function can change concavity without having a local maximum or minimum. For example, the function $y = x^{3}$ has a point of inflection at $x = 0$ but no local extrema.

Answer:

A. The statement is true