# Worksheet: Average and Instantaneous Rates of Change

In this worksheet, we will practice finding the average rate of change of a function between two x-values and using limits to find the instantaneous rate of change.

**Q5: **

For the function , list the average rates of change of over the interval , where , evaluated to 4 decimal places at most.

- A3.6, 3.06, 3.006, 3.0006
- B4.6, 4.06, 4.006, 4.0006
- C3.3, 3.03, 3.003, 3.0003
- D4.3, 4.03, 4.003, 4.0003
- E3.4, 3.04, 3.004, 3.0004

**Q8: **

Determine the average rate of change for when changes from 8 to 8.4.

**Q9: **

Determine the average rate of change function for at .

- A
- B
- C
- D

**Q11: **

Find the average rate of change function of when .

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- B
- C
- D

**Q12: **

Determine the average rate of change function for when changes from to .

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- B
- C
- D

**Q13: **

Determine the average rate of change function for when changes from to .

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- B
- C
- D

**Q14: **

Evaluate the average rate of change of when varies from to .

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- D

**Q15: **

If the average rate of change of the function is 6.67 when varies from 2 to 2.3, find the change in .

**Q17: **

The graph below is of the sales revenue in millions of pounds after months. Find the average rate of change in revenue per month between the and months.

**Q18: **

From the graph of shown, on what interval is the average rate of change of the greatest?

- A
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- D

**Q19: **

From the graph of , determine the intervals where the average rate of change of is constant.

- A,
- B,
- C,
- D,

**Q20: **

Consider the function . What is the average rate of change in over the interval ?

- A
- B
- C47
- D
- E

**Q21: **

The distance traveled by a body in seconds is . What is the average rate of change of when changes from 9 to 13 seconds?

**Q24: **

A metallic cube expands but preserves its shape as it is heated. What is the average rate of change of its surface area when its sides change from 69 cm to 69.7 cm?

**Q25: **

A spherical balloon preserves that shape as it expands. Determine the average rate of change of its surface area when its radius changes from 49 cm to 119 cm.

- A
- B
- C
- D
- E