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

Question B:

`\begin{gathered} f^(\prime)(t)=(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)=(\Delta f(11))/(\Delta t) \\ \\ 1.3=(\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"