# Question about infinitely many times differentiable function.

Could you please give me some hint how to solve this problem:

Suppose $f(x)$ is infinitely many times differentiable function on R, $f(0)=f'(0)=f''(0)=0$.

Prove : for all $A>0$ exists some $c>0$ such as $|f(x)|\le c{|x|}^3$ for all $x\in[-A,A]$.

I could not figure out how to start.

Thanks.

$$f(x) = f(0) + f'(0)x + 1/2 f''(0)x^{2} + 1/3! f'''(\xi)x^{3}$$
s.t. $f'''(x)$ is continuous.