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    Differential equations

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    f(x) = (x^2)sin(1/x)+x if x doesn't equal 0
    f(x) = 0 if x=0

    Prove that the function f:R-> R is differentiable and that f'(0)=1. Also prove that there is no neighbourhood I of 0 such that the function f:I->R is increasing.

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    Solution Summary

    This is a proof regarding differentiability of a function.