QuestionOctober 2, 2026

(1 point) 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? square ? (Be sure that you are able to give a reason for your answer.) (b) What are the units of f'(35) square help (units) Suppose that vert f'(35)vert =1.5 and f(35)=75 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 square minutes after the coffee was put on the counter, its square square and will square by about v is "? square in the next 15 seconds.

(1 point) 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? square ? (Be sure that you are able to give a reason for your answer.) (b) What are the units of f'(35) square help (units) Suppose that vert f'(35)vert =1.5 and f(35)=75 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 square minutes after the coffee was put on the counter, its square square and will square by about v is "? square in the next 15 seconds.
(1 point) 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? square ? (Be sure that you are able to give a reason for your answer.) (b) What are the units of f'(35) square help (units) Suppose that vert f'(35)vert =1.5 and f(35)=75 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 square minutes after the coffee was put on the counter, its square square and will square by about v is "? square in the next 15 seconds.

Solution
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Answer

(a) Negative; (b) Degrees Celsius per minute; (c) 35; temperature; 75 degrees Celsius; decrease; 0.375 degrees Celsius. Explanation 1. Determine the sign of f'(t) The temperature of the coffee decreases over time, so f'(t) is **negative**. 2. Determine the units of f'(35) f'(t) represents the rate of change of temperature with respect to time. Therefore, the units are **degrees Celsius per minute**. 3. Analyze the given information Given \vert f'(35)\vert = 1.5, this means the temperature decreases at a rate of 1.5 degrees Celsius per minute. At t = 35 minutes, f(35) = 75 degrees Celsius. 4. Fill in the blanks At **35** minutes after the coffee was put on the counter, its **temperature** is **75 degrees Celsius** and will **decrease** by about **0.375 degrees Celsius** in the next 15 seconds.

Explanation

1. Determine the sign of $f'(t)$<br /> The temperature of the coffee decreases over time, so $f'(t)$ is **negative**.<br /><br />2. Determine the units of $f'(35)$<br /> $f'(t)$ represents the rate of change of temperature with respect to time. Therefore, the units are **degrees Celsius per minute**.<br /><br />3. Analyze the given information<br /> Given $\vert f'(35)\vert = 1.5$, this means the temperature decreases at a rate of 1.5 degrees Celsius per minute. At $t = 35$ minutes, $f(35) = 75$ degrees Celsius.<br /><br />4. Fill in the blanks<br /> At **35** minutes after the coffee was put on the counter, its **temperature** is **75 degrees Celsius** and will **decrease** by about **0.375 degrees Celsius** in the next 15 seconds.
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