Chapter 4.2, Problem 55E

Use the Mean Value Theorem to prove that $1+\frac{a}{2}>\sqrt{1+a}$ for a > 0. (Hint: For a given value of a > 0. let $f\left(x\right)=\sqrt{1+x}$ on [0, a] and use the fact that $\sqrt{1+c}>1$, for c > 0.)