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    Determine all points x at which f is differentiable.

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    Let f(x) = { x|x| if x is rational
    0 if x is irrational

    determine all points x at which f is differentiable.

    © BrainMass Inc. brainmass.com March 6, 2023, 1:13 pm ad1c9bdddf

    Solution Preview

    f(x) = x*|x| : if x is rational
    and = 0 : if x is irrational

    In such problem before going for differentiability, go for continuity.
    for x = a (a positive rational number) != 0
    Right hand limit (RHL):
    Lt (h->0) f(a+h) = 0
    ( because, a+h can be any irrational ...

    Solution Summary

    The points at which a function is differentiable is determined. Rational and irrational functions are differentiated.