## Calculus 10th Edition

Being a polynomial, $f(x)$ is continuous for all values of $x$ and differentiable at every value of $x$ and hence Rolle's theorem can be applied. Let the three roots be $\alpha, \beta,$ and $\gamma$ such that $\alpha\lt\beta\lt\gamma\to$ Rolle's Theorem guarantees the existence of a horizontal tangent over the interval $[\alpha, \beta]$ and another over the interval $[\beta, \gamma]$.