It is given that $|f''(x)|<=M$ for all $x$, and $f(0)=f'(0)=0$. Then prove that $|f(x)|\leq\frac{Mx^2}{2}$ for all $x$.
What I think about was by using the Mean Value Theorem twice, and then I will get $|f(x)|\leq Mx^2$ with no $\frac{1}{2}$. And I do not know if I use the MVT twice whethere there would be any mistake.
Is there any way other than the MVT to solve this problem? What I also considered were the Fundamental Theorem of Calculus and the Taylor's Theorem. But still, feel not too good about them.
Anyone offers a hint?