Interpret a derivative as a rate of change in context

Question 1

V(t) is the number of users of an app after t days. V′(11) = 19. What does this mean?

• A. On day 11, users are increasing at about 19 per day
• B. The average rate over the whole period
• C. The total change since the start
• D. There are 19 users on day 11

Question 2

The cost (in dollars) of making x phone cases is C(x) = x² + 23x + 200. Use C′(6) to estimate the extra cost of making one more case after 6.

Answer 

Question 3

B(h) is a phone's battery level (%) after h hours. B′(8) = −1. What does this mean?

• A. The average rate over the whole period
• B. The total change since the start
• C. At that moment the battery is falling by about 1 percentage points per hour
• D. The battery has 1% left

Question 4

The cost (in dollars) of making x phone cases is C(x) = x² + 53x + 200. Use C′(17) to estimate the extra cost of making one more case after 17.

Answer 

Question 5

T(m) is the temperature (°C) of a drink m minutes after it is made. T′(20) = −4. What does this mean?

• A. At 20 minutes, the drink is cooling at about 4 °C per minute
• B. The average rate over the whole period
• C. The drink is at 4 °C after 20 minutes
• D. The total change since the start

Question 6

The cost (in dollars) of making x phone cases is C(x) = 2x² + 42x + 200. Use C′(13) to estimate the extra cost of making one more case after 13.

Answer 

Question 7

B(h) is a phone's battery level (%) after h hours. B′(8) = −7. What does this mean?

• A. The battery has 7% left
• B. At that moment the battery is falling by about 7 percentage points per hour
• C. The total change since the start
• D. The average rate over the whole period

Question 8

The cost (in dollars) of making x phone cases is C(x) = 4x² + 28x + 200. Use C′(17) to estimate the extra cost of making one more case after 17.

Answer 

Question 9

B(h) is a phone's battery level (%) after h hours. B′(9) = −8. What does this mean?

• A. The average rate over the whole period
• B. The total change since the start
• C. The battery has 8% left
• D. At that moment the battery is falling by about 8 percentage points per hour

Question 10

The cost (in dollars) of making x phone cases is C(x) = x² + 36x + 200. Use C′(22) to estimate the extra cost of making one more case after 22.

Answer 

Question 11

V(t) is the number of users of an app after t days. V′(7) = 26. What does this mean?

• A. The total change since the start
• B. There are 26 users on day 7
• C. The average rate over the whole period
• D. On day 7, users are increasing at about 26 per day

Question 12

The cost (in dollars) of making x phone cases is C(x) = 4x² + 41x + 200. Use C′(20) to estimate the extra cost of making one more case after 20.

Answer 

Question 13

B(h) is a phone's battery level (%) after h hours. B′(7) = −7. What does this mean?

• A. The average rate over the whole period
• B. The battery has 7% left
• C. The total change since the start
• D. At that moment the battery is falling by about 7 percentage points per hour

Question 14

The cost (in dollars) of making x phone cases is C(x) = 4x² + 27x + 200. Use C′(21) to estimate the extra cost of making one more case after 21.

Answer 

Question 15

T(m) is the temperature (°C) of a drink m minutes after it is made. T′(30) = −3. What does this mean?

• A. At 30 minutes, the drink is cooling at about 3 °C per minute
• B. The average rate over the whole period
• C. The total change since the start
• D. The drink is at 3 °C after 30 minutes

Question 16

The cost (in dollars) of making x phone cases is C(x) = 2x² + 30x + 200. Use C′(14) to estimate the extra cost of making one more case after 14.

Answer