Home > CALC > Chapter 8 > Lesson 8.1.3 > Problem8-35

8-35.

Is there a $c$ on the interval $[0,1]$ for $f(x) = x^2 − x$ where $f^\prime(c) = 0$ ? Justify your answer.

If $f(x)$ is continuous AND differentiable on the given domain, then the Mean Value Theorem will apply.