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Math Help - Quotient Rule for first derivative help.

  1. #1
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    Quotient Rule for first derivative help.

    I'm not sure about the result.

    f(x)= (x3+x2)/(x2-4)

    =(x2-4)(3x2+2x) - (x3+x2)(2x) / (x2-4)2

    =(3x4+2x3-12x2-8x) - (2x4 + 2x3) / (x2-4)2

    =(x4-12x2-8x) / (x2-4)2

    Would this be the simplified first derivative?
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  2. #2
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    Re: Quotient Rule for first derivative help.

    looks ok to me ...
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    Re: Quotient Rule for first derivative help.

    Thanks. Now for finding a possible critical value for increasing and decreasing intervals, I would take the numerator = 0. I'm having trouble on how I should go about that. I've looked up information on how to do critical values, but each has you factoring it down into (x-1) type terms. Meanwhile I have, x4-12x2-8x = 0. I can't factor out anything more than x.
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    Re: Quotient Rule for first derivative help.

    Let y= x^2, so the equation becomes y^2- 12y- 8= 0. Solve that for y then solve x^2= y for x.
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    Re: Quotient Rule for first derivative help.

    Quote Originally Posted by mettler View Post
    Thanks. Now for finding a possible critical value for increasing and decreasing intervals, I would take the numerator = 0. I'm having trouble on how I should go about that. I've looked up information on how to do critical values, but each has you factoring it down into (x-1) type terms. Meanwhile I have, x4-12x2-8x = 0. I can't factor out anything more than x.
    x(x^3-12x-8) = 0

    the cubic factor has three real roots, but none are rational ... you will most probably have to use technology to find them.
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