Which of the following statements is/are true?

If f '(c) = 0, then f has a local maximum or minimum at x = c.

If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].

The Mean Value Theorem can be applied to f(x) = 1/x2 on the interval [−1, 1].

Question

Which of the following statements is/are true?

If f '(c) = 0, then f has a local maximum or minimum at x = c.

If f is continuous on [a, b] and differentiable on (a, b) and f '(x) = 0 on (a, b), then f is constant on [a, b].

The Mean Value Theorem can be applied to f(x) = 1/x2 on the interval [−1, 1].

mathmate · Answer

The questions contains three topics, each of which must be understood to select/reject each choice. Here are some background material to help you figure out the answer: http://www.math.com/tables/derivatives/extrema.htm https://en.wikipedia.org/wiki/Differentiable_function http://www.sosmath.com/calculus/diff/der11/der11.html