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Math Help - Critical Points Help?

  1. #1
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    Critical Points Help?

    Hey guys,

    I'm just having a bit of trouble with this one question. I'm trying to follow my teacher's notes but I don't have an example like it, so it's a little difficult for me.

    Here's the question:

    Find the critical numbers of the function. (Enter your answers as fractions.) F(x) = x4/5(x - 1)2



    Here's what I've got so far:

    f'(x) = 4/5x^-1/5 * (x-1)^2 - x^4/5
    f'(x) = x^-1/5 (4/5(x-1)^2 -x^3/5)
    f'(x) = x^-1/5 (4/5(x^2-2x+1) - x^3/5)
    f'(x) = x^-1/5 (4/5x^2 - 13/5x^3/5 + 4/5) I combined the -8/5x with -x^3/5

    I don't think I'm doing this right, however. A little bit of guidance would be appreciated?


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  2. #2
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    Quote Originally Posted by dark-ryder341 View Post
    Hey guys,

    I'm just having a bit of trouble with this one question. I'm trying to follow my teacher's notes but I don't have an example like it, so it's a little difficult for me.

    Here's the question:

    Find the critical numbers of the function. (Enter your answers as fractions.) F(x) = x4/5(x - 1)2



    Here's what I've got so far:

    f'(x) = 4/5x^-1/5 * (x-1)^2 - x^4/5
    f'(x) = x^-1/5 (4/5(x-1)^2 -x^3/5)
    f'(x) = x^-1/5 (4/5(x^2-2x+1) - x^3/5)
    f'(x) = x^-1/5 (4/5x^2 - 13/5x^3/5 + 4/5) I combined the -8/5x with -x^3/5

    I don't think I'm doing this right, however. A little bit of guidance would be appreciated?


    f(x) = x^{\frac{4}{5}} (x-1)^2

    product rule ...

    f'(x) = x^{\frac{4}{5}} \cdot 2(x-1) + (x-1)^2 \cdot \frac{4}{5}x^{-\frac{1}{5}}

    continue ...
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