19.5.3 Compactness

Problem: Prove that in the space \( C[-1 ; 2] \) relatively compact (precompact) set \[ E=\left\{\varphi \in C[-1 ; 2],\left|\int_{-1}^{2} x \varphi(x) d x\right| \leq 3,\left|\varphi^{\prime}(x)\right| \leq 3\right\} . \]