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Math Help - Differentiability

  1. #1
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    Differentiability

    Find all values of x for which the function is differentiable.

    y= \frac {x^3 - 8}{x^2 -4x-5}

    Easy way out is graphing.
    Is there an algebraic way of figuring this out?

    It looks to me that x=2 does not work, for the nominator equals 0.
    x=5 appears to give on discontinuity, as the denominator is 0.

    Anything I missed?

    Thanks.
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  2. #2
    MHF Contributor kalagota's Avatar
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    Quote Originally Posted by Truthbetold View Post
    Find all values of x for which the function is differentiable.

    y= \frac {x^3 - 8}{x^2 -4x-5}

    Easy way out is graphing.
    Is there an algebraic way of figuring this out?

    It looks to me that x=2 does not work, for the nominator equals 0.
    x=5 appears to give on discontinuity, as the denominator is 0.

    Anything I missed?

    Thanks.
    note that one of the criteria of a function to be differentiable is continuity.
    in that case, the values where the denominator is zero are not included, thus your function is differentiable at x=2; and x=5 and x=-1 are not included.
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