Question 1

Suppose $$f(t) is $$the distance in cm from the origin of a rat after $$t$$ seconds, as shown in the first graph. Which of the following is the largest value?

A: The speed of the rat at $$t=1
B$$: The speed of the rat at $$t=2
C$$: The speed of the rat at $$t=3
D$$: The average speed of the rat between $$t=2$$ and $$t=3
E$$: The average speed of the rat between $$t=3$$ and $$t=4$$

Accepted Answer

The average speed of the rat between $$t=3$$ and $$t=4$$

Question 2

Suppose $$f(t) is $$the temperature in degrees Fahrenheit at $$t$$ hours after midnight. What does $$f'(7) = 3$$ mean?

Accepted Answer

At 7 hours after midnight, the temperature is increasing at a rate of 3 degrees Fahrenheit per hour.

Question 3

Suppose $$g(t) is $$the distance from the origin of a rat on the $$x-$$axis after $$t$$ seconds. What does $$g'(9) = -5$$ mean?

Accepted Answer

At $$t=9$$ seconds, the rat is moving toward the origin at 5 cm/sec.

Question 4

Suppose $$f(t) is $$the population of the ancient city of Lyrad in year $$t. $$What does $$f'(1650) = 100$$ mean?

Accepted Answer

In the year 1650, the population was increasing at a rate of 100 people per year.

Question 5

Suppose $$f(1550) = 3000$$ and $$f'(1650) = 100$$ for the population of Lyrad. Which of the following is true?

Accepted Answer

None of the above.

Question 6

Suppose $$f(0) = 50$$ and $$f(10) = 70. $$Which of the following is possible?

Accepted Answer

It is possible that $$f'(0) = -8$$

Question 7

Suppose $$f(x) is $$the monthly cost of heating a house to $$x$$ degrees Fahrenheit. What does $$f'(70) = 9$$ mean in the context of the second graph?

Accepted Answer

At 70°F, the monthly cost is increasing by $9 for each additional degree Fahrenheit.

Question 8

Suppose $$f(3) = 5$$ and $$f'(3) = 2. $$Which of the following statements is true about the third graph?

Accepted Answer

At $$x=3$$, the tangent line to $$f(x)$$ has a slope of 2.

Question 9

Suppose $$f(t) is $$the temperature of an oven in degrees Celsius after $$t$$ minutes. What does $$f'(3) = 15$$ mean?

Accepted Answer

At 3 minutes, the oven's temperature is increasing at a rate of 15°C per minute.

Question 10

Suppose $$f(x) is $$the number of heartbeats per minute with $$x mg of $$adrenaline in the blood. What does $$f'(5) = 2$$ mean?

Accepted Answer

At 5 mg of adrenaline, the heart rate increases by 2 bpm for each additional mg of adrenaline.

Question 11

Suppose $$f(x) is $$the monthly cost of heating a house to $$x$$ degrees Fahrenheit, and $$f(70) = 140. $$What does this mean?

Accepted Answer

Heating the house to 70°F costs $140 per month.

Question 12

Suppose $$f(t) is $$the population of the ancient city of Lyrad in year $$t. $$What does $$f(1550) = 900$$ mean?

Accepted Answer

In the year 1550, the population was 900.

Question 13

Suppose $$f(t) is $$the temperature in degrees Fahrenheit at $$t$$ hours after midnight. What does $$f(7) = 48$$ mean?

Accepted Answer

At 7 hours after midnight, the temperature is 48°F.

Question 14

Suppose $$f(t) is $$the temperature in degrees Fahrenheit at $$t$$ hours after midnight. What does $$f(9) = -5$$ mean?

Accepted Answer

At 9 hours after midnight, the temperature is -5°F.

Question 15

Suppose $$f(x) is $$the monthly cost of heating a house to $$x$$ degrees Fahrenheit. If the slope at $$x=70 is$$ $$9$$ $$\$$/^\circ F$, what is the practical meaning of this slope?

Accepted Answer

For each additional degree above 70°F, the monthly cost increases by $9.

Question 16

Suppose $$f(3) = 5$$ and $$f'(3) = 2. $$What is the equation of the tangent line to $$f(x) at$$ $$x=3$$?

Accepted Answer

$$y = 2(x-3) + 5$$

Lecture 16

Study Guide - Practice Questions

Study Guide - Flashcards