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Homework Help: The rate at which the coffee is cooling

  1. Oct 11, 2009 #1
    1. The problem statement, all variables and given/known data

    The temperature, H, in degrees Celsius, of a hot cup of coffee placed on the kitchen counter is given by H=f(t), where t is in minutes since the coffee was put on the counter.

    Is f'(t) positive or negative?

    What are the units of f'(20)?

    What is its practical meaning in terms of the temperature of the coffee?
    -The rate of cooling of the coffee is 20 degrees per minute
    -The temperature of the coffee after 20 minutes
    -The temperature of the coffee is 20 degrees
    -The rate at which the coffee is cooling, in degrees per minute, 20 minutes after the cup is put on the counter.

    2. Relevant equations

    3. The attempt at a solution
    I'm lost.
  2. jcsd
  3. Oct 11, 2009 #2
    Re: Derivative

    Think Newton's Law of Cooling.
  4. Oct 11, 2009 #3


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    Staff Emeritus
    Science Advisor
    Gold Member

    Re: Derivative

    This is a math question not a physics question. Common sense and an understanding of the derivative is all that is required.

    If f'(t) is positive, what can you say about f(t)? If f'(t) is negative, what can you say about f(t)?

    We're not going to do your work for us, you have to show us what you've tried to do so far. Knowing what the units of f'(20) are just requires looking at the fraction that defines the derivative and spotting what the units are
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