Explore BrainMass

Explore BrainMass

    Determine all points x at which f is differentiable.

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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 4, 2021, 5:44 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/determine-all-points-differentiable-8944

    Solution Preview

    because,
    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.

    $2.49

    ADVERTISEMENT