Question

The temperature, HH, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H=f(t)H=f(t), where tt is in minutes since the coffee was put on the counter. (a) Is f′(t)f′(t) positive or negative? negative (Be sure that you are able to give a reason for your answer.) (b) What are the units of f′(20)f′(20)? help (units) Suppose that |f′(20)|=1.5|f′(20)|=1.5 and f(20)=56f(20)=56. 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 ? by about in the next 45 seconds.

Answer 1

A) f'(t) is negative

B) degc/min

c ) At 20 minutes after the coffee was put on the counter its temperature is 56degc and will decrease by about 1.125 in the next 45 seconds

Explanation:

A ) f'(t) is Negative because as the cup of coffee is placed on the counter there is loss of heat from the cup of coffee to the surrounding as t increases hence f'(t) is negative

B ) The units of f'(20) = degc/min

C) At ║f'(20)║ = 1.5 and f'(20) = 56

║f'(20)║ = 1.5 represents the rate of change of temp every 20 minutes = 1.5

therefore after 45 seconds = 3/4 mins. change in temp = (3/4 * 1.5) = 1.125

At 20 minutes after the coffee was put on the counter its temperature is 56degc and will decrease by about 1.125 in the next 45 seconds