## Calculus 10th Edition

Let $a$ and $b$ be any two x-values in the domain of $f(x).$ Using Rolle's Theorem over the interval $[a. b]\to$ $f'(x)=\dfrac{f(b)-f(a)}{b-a}\to$ $0=\dfrac{f(b)-f(a)}{b-a}=\to f(b)=f(a)\to f(x)$ is constant.