Chapter 3 - Applications of Differentiation - 3.2 The Mean Value Theorem - 3.2 Exercises - Page 219: 3

Rolle's Theorem does not apply because $f(x)$ is discontinuous at $f(0)$

We look at the function and its domain, and its endpoints $f(x)=|\frac{1}{x}|, [-1,1]$ $f(-1)=f(1)=1)$ However, since there is a vertical asymptote at $f(0)$, that makes the graph discontinuous over the interval $[-1,1]$, and Rolle's Theorem does not apply.