# Real Analysis: Differentiation

If I let the function f:R->R have two derivatives with f(0) = 0 and f'(x) <= f(x) for all x in R.

Is f(x) = 0 for all x in R

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#### Solution Preview

No

Here is a counter example

We define f(x) as follows:

if x>=0, f(x)=0

if x<0, f(x)=x^4 ...

#### Solution Summary

A counter-example is used to disprove a statement about a function. A function for two derivatives are analyzed.

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