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Math Help - Applications of Derivatives

  1. #1
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    Applications of Derivatives

    A dose, D of a drug causes a temperature change, T, in a patient. For C a positive constant, T is given by

     T = ( \frac{C}{2} - \frac{D}{3} ) D^3.

    (a) What is the rate of change of temperature change with respect to dose?

    (b) For what doses does the temperature change increase as the dose increases?

    I think I have this one correct as well, I'm just kind of fuzzy on this material, so I'd like some reassurance.

    (a) This part is easy.
     \frac{dT}{dD} = \frac{3C}{2} D^2 - \frac{4}{3} D^3

    (b) This part I'm not too sure about.
     \frac{3C}{2} D^2 - \frac{4}{3} D^3 > 0
     D^2 ( \frac{3C}{2} - \frac{4}{3} D) > 0
     D < \frac{9C}{8}

    Is this correct? Thanks.
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  2. #2
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    Quote Originally Posted by Jacobpm64 View Post
    A dose, D of a drug causes a temperature change, T, in a patient. For C a positive constant, T is given by

     T = ( \frac{C}{2} - \frac{D}{3} ) D^3.

    (a) What is the rate of change of temperature change with respect to dose?

    (b) For what doses does the temperature change increase as the dose increases?

    I think I have this one correct as well, I'm just kind of fuzzy on this material, so I'd like some reassurance.

    (a) This part is easy.
     \frac{dT}{dD} = \frac{3C}{2} D^2 - \frac{4}{3} D^3

    (b) This part I'm not too sure about.
     \frac{3C}{2} D^2 - \frac{4}{3} D^3 > 0
     D^2 ( \frac{3C}{2} - \frac{4}{3} D) > 0
     D < \frac{9C}{8}

    Is this correct? Thanks.
    Hello,

    your calculations are correct. To make sure that your final result isn't misread I would write:  0 < D < \frac{9C}{8}

    (I know it is quite impossible to get a negative dose, but only to be on the safe side I would write it this way)

    EB
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