### Home > CALC > Chapter 6 > Lesson 6.1.3 > Problem 6-40

6-40.

If *f*(*x*)* *is a continuous function, *f* ′(2) = −1, and *f* ′(3) = 1, does there have to be an *x*-value *a *such that 2 < *a < *3 and *f* ′(*a*) = 0 ? Draw a sketch to support your explanation. Homework Help ✎

A function may be continuous without being differentiable at all points.