### Home > APCALC > Chapter 6 > Lesson 6.1.3 > Problem6-40

6-40.

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

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