Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Functions

Example 4 from Algebra and Trigonometry, 3.3 Rates of Change and Behavior of Graphs

Computing Average Rate of Change for a Function Expressed as a Formula

Compute the average rate of change of $f (x) = x^{2} - \frac{1}{x}$ on the interval $[2, 4].$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
We can start by computing the function values at each endpoint of the interval.

$\begin{matrix} Average rate of change & = & \frac{f (4) - f (2)}{4 - 2} \\ = & \frac{\frac{63}{4} - \frac{7}{2}}{4 - 2} \\ = & \frac{\frac{49}{4}}{2} \\ = & \frac{49}{8} \end{matrix}$
Now we compute the average rate of change.

$\begin{matrix} Average rate of change & = & \frac{f (4) - f (2)}{4 - 2} \\ = & \frac{\frac{63}{4} - \frac{7}{2}}{4 - 2} \\ = & \frac{\frac{49}{4}}{2} \\ = & \frac{49}{8} \end{matrix}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the average rate of change of $f (x) = x - 2 \sqrt{x}$ on the interval $[1, 9] .$

How did it go?

PreviousComputing Average Rate of Change from a Table Next Finding the Average Rate of Change of a Force

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.3, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.