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. (a) Is 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'(10)? degC/min Suppose that |f'(10)| = 1.3 and f(10) = 52. 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 10 minutes after the coffee was put on the counter, its temperature is and will decrease by about in the next 30 seconds. 

          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.

(a) Is 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'(10)? degC/min

Suppose that |f'(10)| = 1.3 and f(10) = 52. 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 10 minutes after the coffee was put on the counter, its temperature is and will decrease by about in the next 30 seconds.
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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. (a) Is 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'(10)? degC/min Suppose that |f'(10)| = 1.3 and f(10) = 52. 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 10 minutes after the coffee was put on the counter, its temperature is and will decrease by about in the next 30 seconds.

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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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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. (a) Is f'(t) positive or negative? (Be sure that you are able to give a reason for your answer.) (b) What are the units of f'(10)? Suppose that |f'(10)| = 1.3 and f(10) = 52. 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 10 minutes after the coffee was put on the counter, its temperature is and will decrease by about in the next 30 seconds.
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Transcript

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00:01 So in this question, the temperature h in degrees celsius of a cup of coffee placed on the kitchen counter is given by h equals f of t, where t is in minutes since the coffee was put on the counter.
00:12 In part a, they say, is f prime of t positive or negative? you are correct that f prime of t is negative.
00:20 Why is that the case? the reason is because the temperature of the coffee is decreasing, so my rate of change should be negative this time.
00:30 Now, i agree that the units on f prime of 10 should be in degrees celsius per minute.
00:38 It is a rate of change, so it's units of h or units of f degrees celsius, divided by units of time, minutes.
00:47 Now, suppose that the absolute value of f prime of 10 is 1 .3, and the f of 10 is 52.
00:55 What does this mean? it means, indeed, that at 10 minutes after the coffee was put on the counter, its temperature is what? well, that's the value of the function.
01:10 So the value of the function is 52.
01:14 So 52 degrees celsius is the temperature of the coffee at 10 minutes.
01:22 And that temperature will indeed decrease...
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