Question

The temperature, T , in degrees Fahrenheit, of a cold yam placed in a hot oven is given by T=f(t) , where t is the time in minutes since the yam was put in the oven.

What is the sign of f'(t)? Why?

What are the units of f'(20)? What is the practical meaning of the statement f' (20)=2?

Answer 1

a) positive

b)

`^\circ F\text{ per Minute}`

c) Interpretation of f'(20)=2

Explanation:

We are given the following in the question:

`T=f(t)`

where T is the temperature in degrees Fahrenheit of a cold yam placed in a hot oven and t is the time in minutes since the yam was put in the oven.

a) sign of f'(t)

f'(t) will represent the rate of change in temperature.

f'(t) will represent the change in temperature of yam when 1 minute has passed since it was kept in oven.

Since the temperature will always increase in oven, f'(t) will have a positive sign.

b) units of f'(20)

Since, f'(t) represent the rate of change in temperature. the unit will be

`\frac{\text{degrees Fahrenheit}}{\text{Minute}}`

That is degrees Fahrenheit per minute.

c) f'(20)=2

f'(20) will tell the change in temperature when 20 minutes have passed after the yam has been kept in oven.

Thus, the given statement means that 20 minutes after the yam was kept for in the oven, the temperature of yam was increasing by 2 degree Fahrenheit per minute.