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Math Help - need help optimization

  1. #1
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    need help optimization

    Suppose that body temperature 1 hour afer receiving x mg of drug is given by
    T(x)=102-(1/6) x^2(1-x/9)
    for 0<=x<=6.The absolute value of the derivative,|T'(x)| is defined as sensitivty of the body to the drug dosage.Find the dosage that maximize sensitivity
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bobby77 View Post
    Suppose that body temperature 1 hour afer receiving x mg of drug is given by
    T(x)=102-(1/6) x^2(1-x/9)
    for 0<=x<=6.The absolute value of the derivative,|T'(x)| is defined as sensitivty of the body to the drug dosage.Find the dosage that maximize sensitivity
    Sketch y=T(x), you will find that it gas a maximum at x=0, and a minimum at x=6,
    and its derivative is negative on (0,6). So |T'(x)|=-T'(x) on the interval.

    So now you are looking for the maximum of -T'(x). So differentiate it and set
    that derivative to zero solve for x, and substitute back into -T'(x) to find the
    maximum. So you need to find the solutions of:

    T''(x)=0.

    RonL
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