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Math Help - Interval Question

  1. #1
    QED
    QED is offline
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    Interval Question

    I think maybe I'm differentiating this wrong...

    Find the intervals where the function is increasing and decreasing for:

    g(x) = x / (x+1)^2

    ---------------

    I differentiated it as:

    (x+1)^2 - 2x^2(x+1) /
    (x+1)^4

    Right? What are the intervals?

    Thanks!
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  2. #2
    MHF Contributor

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    Quote Originally Posted by QED View Post
    I think maybe I'm differentiating this wrong...

    Find the intervals where the function is increasing and decreasing for:

    g(x) = x / (x+1)^2

    ---------------

    I differentiated it as:

    (x+1)^2 - 2x^2(x+1) /
    (x+1)^4

    Right?
    No, that is not correct. Assuming you mean ((x+1)^2- 2x^2(x+1))/(x+1)^4, you should not have that "^2" in "-2x^2(x+1)". The derivative of (x+1)^2 is 2(x+1) and, using the quotient rule, you just multiply that derivative by the numerator, x.

    What are the intervals?
    Thanks!
    Well, why did you differentiate? What is true about the derivative of a function where the function is increasing? What if the function is decreasing?
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