Question

The temperature, H, in degrees Celsius, of a cup of coffee placed on che kitchen counter to cool is given by H = f(t), where t is in minutes since the coffee was put on the counter.(b) What are the units of f'(11)? = ____ units

Answer 1

Solution

Question B:

$\begin{gathered} f^{\prime}(t)=\frac{df(t)}{dt} \\ \\ f(t)\text{ is the temperature in degree Celsius} \\ \\ \therefore f^{\prime}(t)\text{ has a unit of }Celsius\text{ / Minute} \end{gathered}$

- We have been given

$\begin{gathered} f(11)=79 \\ |f^{\prime}(11)|=1.3 \end{gathered}$

- This implies that

"At 11 minutes after the coffee was put on the counter, its temperature is 79 "

- Also,

$\begin{gathered} f^{\prime}(11)=1.3 \\ \text{ Thus, in the next 90 seconds or 1.5 minutes} \\ f^{\prime}(11)=\frac{\Delta f(11)}{\Delta t} \\ \\ 1.3=\frac{\Delta f(11)}{1.5} \\ \\ \therefore\Delta f(11)=1.95 \end{gathered}$

- This implies that the "temperature will decrease by 1.95 in the next 90 seconds"