Home > CALC > Chapter 6 > Lesson 6.1.3 > Problem6-40

6-40.

If $f(x)$ is a continuous function, $f^\prime(2) = −1$, and $f^\prime(3) = 1$, does there have to be an $x$-value a such that $2 < a < 3$ and $f^\prime(a) = 0$? Draw a sketch to support your explanation.

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