The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen

Question

The temperature, H, in degrees Celsius, of a 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.

What are the units of f'(25)?

Suppose that |f'(25)|=1.4 and f(25)=68. Fill in the blanks (including units where needed) and select the appropriate terms to complete the following statement about the temperature of the coffee in this case.

At _____? minutes after the coffee was put on the counter, its temperature is _____? and will decrease by about ________? in the next 30 seconds.

Explanation / Answer

any derivative is also know as "rate of change" so f '(t) is the rate of change of H with respect to t (degC/min). since f '(25)=0.4 at 77degC the rate of change is -0.4 degC/min (i put a negative sign because the temperature is decreasing) so then in the next 15 seconds the temp will have decreased by 0.1 degC

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