On the fourth page of their 1967 paper Local Behavior of Solutions of Quasilinear Parabolic Equations, Aaronson and Serrin comment: "Consider a strongly differentiable function $w$ of the real variable $x$, $0 < x < d$. Then obviously

$$|w(x)|^{2} \leq \frac{2}{d}\int_{0}^{d}|w|^{2}\ dx + 2d\int_{0}^{d}|w_{x}|^{2}\ dx$$

and..."

And obviously I don't get it, and am wondering what background I need to fill in before I can read this paper.