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    Real Analysis: Differentiation

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    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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    https://brainmass.com/math/real-analysis/real-analysis-differentiation-function-9563

    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.

    $2.49

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