Share
Explore BrainMass

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

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.

$2.19