## Problem 753

Let $c$ be a fixed positive number. Let $X$ be a random variable that takes values only between $0$ and $c$. This implies the probability $P(0 \leq X \leq c) = 1$. Then prove the next inequality about the variance $V(X)$.
$V(X) \leq \frac{c^2}{4}.$

## Problem 650

Find a quadratic function $f(x) = ax^2 + bx + c$ such that $f(1) = 3$, $f'(1) = 3$, and $f^{\prime\prime}(1) = 2$.

Here, $f'(x)$ and $f^{\prime\prime}(x)$ denote the first and second derivatives, respectively.