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Math Help - Find the critical numbers of a function

  1. #1
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    Find the critical numbers of a function

    I know to find the critical numbers you'd find the first derivative and solve for where it is 0, but I just can't get the right answer for this one

    f(x)= x^(1/5) - x^(-4/5)
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  2. #2
    Member anonimnystefy's Avatar
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    Re: Find the critical numbers of a function

    what did you get for the derivative? maybe the problem is in what you got.
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  3. #3
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    Re: Find the critical numbers of a function

    f'(x) = 1/[5x^(4/5)] + 4/[5x^(9/5)]
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  4. #4
    Member anonimnystefy's Avatar
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    Re: Find the critical numbers of a function

    what did you do when you set that equal to zero?
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  5. #5
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    Re: Find the critical numbers of a function

    First I factored out 1/5x^4/5

    So I had: 1/[5x^(4/5)] x (1 + 4/x)

    Then I set that to 0, but the first part is never zero so I just solved for where 1 + 4/x is 0 and got -4. Shouldn't that be the right answer?
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  6. #6
    Super Member Quacky's Avatar
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    Re: Find the critical numbers of a function

    f'(x)=\frac{1}{5x^{\frac{4}{5}}}+\frac{4}{5x^\frac  {9}{5}}

    0=\frac{1}{5x^{\frac{4}{5}}}+\frac{4}{5x^\frac{9}{  5}}

    0=\frac{1}{5x^{\frac{4}{5}}}(1+\frac{4}{x})

    What is the given answer? Because as far as I can tell, having checked, and having checked again, there's no problem with your work, unless I'm missing something.
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