Interpret a derivative as a rate of change in context

Question 1

B(h) is a phone's battery level (%) after h hours. B′(8) = −5. What does this mean?

• A. The battery has 5% left
• B. The total change since the start
• C. At that moment the battery is falling by about 5 percentage points per hour
• D. The average rate over the whole period

Question 2

The cost (in dollars) of making x phone cases is C(x) = 3x² + 15x + 200. Use C′(24) to estimate the extra cost of making one more case after 24.

Answer 

Question 3

B(h) is a phone's battery level (%) after h hours. B′(3) = −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 4

The cost (in dollars) of making x phone cases is C(x) = 3x² + 57x + 200. Use C′(21) to estimate the extra cost of making one more case after 21.

Answer 

Question 5

T(m) is the temperature (°C) of a drink m minutes after it is made. T′(26) = −6. What does this mean?

• A. The average rate over the whole period
• B. The drink is at 6 °C after 26 minutes
• C. At 26 minutes, the drink is cooling at about 6 °C per minute
• D. The total change since the start

Question 6

The cost (in dollars) of making x phone cases is C(x) = x² + 53x + 200. Use C′(5) to estimate the extra cost of making one more case after 5.

Answer 

Question 7

T(m) is the temperature (°C) of a drink m minutes after it is made. T′(16) = −1. What does this mean?

• A. The drink is at 1 °C after 16 minutes
• B. At 16 minutes, the drink is cooling at about 1 °C per minute
• 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) = x² + 27x + 200. Use C′(24) to estimate the extra cost of making one more case after 24.

Answer 

Question 9

B(h) is a phone's battery level (%) after h hours. B′(7) = −9. What does this mean?

• A. The average rate over the whole period
• B. At that moment the battery is falling by about 9 percentage points per hour
• C. The battery has 9% left
• D. The total change since the start

Question 10

The cost (in dollars) of making x phone cases is C(x) = 4x² + 40x + 200. Use C′(5) to estimate the extra cost of making one more case after 5.

Answer 

Question 11

B(h) is a phone's battery level (%) after h hours. B′(8) = −5. What does this mean?

• A. At that moment the battery is falling by about 5 percentage points per hour
• B. The average rate over the whole period
• C. The battery has 5% left
• D. The total change since the start

Question 12

The cost (in dollars) of making x phone cases is C(x) = 2x² + 29x + 200. Use C′(25) to estimate the extra cost of making one more case after 25.

Answer 

Question 13

T(m) is the temperature (°C) of a drink m minutes after it is made. T′(29) = −9. What does this mean?

• A. The total change since the start
• B. The drink is at 9 °C after 29 minutes
• C. The average rate over the whole period
• D. At 29 minutes, the drink is cooling at about 9 °C per minute

Question 14

The cost (in dollars) of making x phone cases is C(x) = 3x² + 53x + 200. Use C′(7) to estimate the extra cost of making one more case after 7.

Answer 

Question 15

T(m) is the temperature (°C) of a drink m minutes after it is made. T′(12) = −3. What does this mean?

• A. At 12 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 12 minutes

Question 16

The cost (in dollars) of making x phone cases is C(x) = 2x² + 20x + 200. Use C′(6) to estimate the extra cost of making one more case after 6.

Answer