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Homework Help: Rate of change problem

  1. Mar 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Suppose that t hours after a piece of food is put in the fridge its temperature (in Celsius) is

    T(t) = 15 - 3t + [tex]\frac{4}{t - 1}[/tex]

    where 0 [tex]\leq[/tex] t [tex]\leq[/tex] 5.

    Find the rate of change of temperature after one hour.


    3. The attempt at a solution

    Since it's asking for rate of change, I'm guessing I have to find the derivative of the equation with respect to t.


    T(t) = 15 - 3t + [tex]\frac{4}{t - 1}[/tex]

    T`(t) = 0 - 3 + [tex]\frac{0(t - 1) - 1(4)}{(t-1)^{2}}[/tex] (Quotient Rule)

    T`(t) = -3 + [tex]\frac{0 - 4}{(t-1)^{2}}[/tex]

    T`(t) = -3 + [tex]\frac{-4}{(t-1)^{2}}[/tex]

    T`(t) = -3 - [tex]\frac{4}{(t-1)^{2}}[/tex]


    Would I just plug in 1 after this?
     
  2. jcsd
  3. Mar 30, 2008 #2

    HallsofIvy

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    Don't guess! The derivative of a function is its rate of change!


    That's what you would like to do- but this function has serious problem at t= 1. Do you remember that, in order to have a derivative at a point, the function must be continuous there? Are you sure you have copied the problem correctly? That's a very strange temperature function! Isn't it peculiar that the temperature of the food goes up when it is put in the refridgerator?
     
    Last edited by a moderator: Mar 30, 2008
  4. Mar 30, 2008 #3
    Yes, I checked and checked again and that is the equation.

    What if I were to plug in a value slightly greater than 1? Would that give me the rate of change after one hour?
     
    Last edited: Mar 30, 2008
  5. Mar 30, 2008 #4

    HallsofIvy

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    Well, I just don't know what to say about a refrigerator where the temperature goes to infinity in one hour!
     
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