Answer to Question #276070 in Real Analysis for Anaya

Question

Assume that $1<p<+\infty$, a real-valued function $f$ is absolutely continuous on $[a,b]$, and its derivative $f'$ is in $L^p[a,b]$. Prove that $f$ is $\alpha$-Lipschitz, where $\alpha=1/q$, with $q$ being the conjugate exponent of $p$.