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Math Help - Local Extrema Problem

  1. #1
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    Question Local Extrema Problem

    Let f(x)=(x^(4))(2+sinx^(-1)), if x≠0
    ...........0, if x=0

    Prove that f is differentiable on R (the real numbers).
    Prove that f has an absolute minimum at x=0.
    Prove that f ' takes on both positive and negative values in every neighborhood of 0.

    Pretty lost on this problem, I would really appreciate some help please
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  2. #2
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    What is the domain of your function?

    To show a minimum at x=0, solve f'(x)=0
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