Suppose $f''(x)$ exists on the interval $(-1,1)$,$f(0)=f'(0)=0$,and the inequality $|f''(x)|\leqslant|f(x)|+|f'(x)|$ holds on $(-1,1)$; How to prove that $f(x)=0$ on $(-\delta,\delta)$ for some $\delta>0$? Thanks for help.
About mean value theorem
5
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calculus