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Average Rate of Change Practice Problems

Find the outputs at both ends of the interval, subtract them in the same order as the inputs, and divide. The later problems use tables and real-world rates.

  1. 1.

    Find the average rate of change of on .

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    , the slope of the line.

  2. 2.

    Find the average rate of change of on .

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    .

  3. 3.

    Find the average rate of change of on .

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    , , so .

  4. 4.

    Find the average rate of change of on .

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    .

  5. 5.

    Find the average rate of change of on .

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    .

  6. 6.

    Find the average rate of change of on .

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    .

  7. 7.

    A table gives at and at . What is the average rate of change on ?

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    .

  8. 8.

    The temperature was 58 °F at hour 2 and 74 °F at hour 6. What was the average rate of change, in °F per hour?

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    °F per hour.

  9. 9.

    Find the average rate of change of on .

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    .

  10. 10.

    A town had 12,000 residents in 2015 and 15,600 in 2021. What was the average rate of change in residents per year?

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    .

  11. 11.

    A car has gone 55 miles after 1 hour and 175 miles after 3 hours. What was its average speed in mph?

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    mph.

  12. 12.

    Find the average rate of change of on . Give a fraction or 2 decimal places.

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    .
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Average Rate of Change Practice Problems

These problems follow the average rate of change lesson. Only the two endpoints of the interval matter, never the values in between.

The formula

Common mistakes to watch for

  • Subtracting in different orders. Use : the same point comes first on top and bottom.
  • Using -values in the numerator. The numerator is the change in outputs, , not .
  • Forgetting units. Average rate of change has units of output per input, such as metres per second.
  • Expecting it to match the slope everywhere. For a curve it is the slope of the secant line between two points, not the slope at each point.

Frequently Asked Questions

What is the formula for average rate of change?+

(f(b) − f(a)) / (b − a) on the interval [a, b].

Can the average rate of change be negative?+

Yes. A negative rate means the function ended lower than it started on that interval.

How do I type my answers?+

Type numbers without units, fractions like 5/3, and expressions like 2x + h. For intervals use parentheses or brackets and oo for infinity, for example (2, oo).

Calculators for this topic

Average Rate of Change Calculator

More practice problems

Difference Quotient Practice Problems Slope Practice Problems Increasing and Decreasing Intervals Practice Problems