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Math Help - DBL Check My Derivative PLS

  1. #1
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    DBL Check My Derivative PLS

    I have a problem where I need to find where the function is increasing/decreasing, critical values, concavity etc... But I think my first derivative may be wrong.

    Question: g(x)=\frac{4x-2.2}{(4x-4.84)^2}

    Using the quotient formula, I have the following:

    g'(x)=\frac{4*(4x-4.84)^2-2(4x-4.84)*4*(4x-2.2)}{(4x-4.84)^4}

    g'(x)=\frac{4*(-4x-.44)}{(4x-4.84)^3}

    So to find my critical points, I set my numerator to 0.

    -4x-.44=0
    -.44=4x
    -.11=x

    4x-4.84=0
    x=1.21


    I also set my numerator to 0 (something to do with vertical asymtotes but I am not sure why we do this)

    Using a number line, I think the function will be:

    Decreasing: (-infinity, -.11) U (1.21, infinity)
    Increasing: (-.11,1.21)

    Correct?

    I didn't want to go any further to test for concavity just in case my 1st derivative was wrong.

    TIA
    Last edited by mvho; July 9th 2009 at 01:14 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    algebra looks, just saw a few typos.

    you mean g', not g
    and you wrote 4.8 instead of 4.84 on the fifth line
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  3. #3
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    Thanks, I've made the changes but it appears my critical numbers are wrong?

    Don't I just set -4x-.44=0?
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  4. #4
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    Ok, now I am having trouble finding my 2nd derivative and testing for concavity!

    This is what I have so far:

    g"(x)=\frac{(4x-4.84)^3(-16)-(-4x-.44)(4)(3(4x-4.84)^2(4))}{(4x-4.84)^3}

    This is up to where I know I have not made any mistakes yet..
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