Difference Quotient


Examples, solutions, videos, worksheets, and activities to help PreCalculus students learn how to find the difference quotient of a function.




Share this page to Google Classroom

Related Pages
More Lessons for PreCalculus
Math Worksheets

The following figures show the Difference Quotient formula and graph. Scroll down the page for examples and step by step solutions.

Difference Quotient Formula
 

Computing Difference Quotients
To find the slope of the secant line between two points in a function, we use difference quotients. Difference quotients are used with limits in the definition of the derivative and are important to understand, but can be difficult to compute and simplify. We can simplify difference quotients into a formula for finding the slope of a secant line.

The Difference Quotient
This video gives the formula for the difference quotient (the subtraction fraction) and do a couple examples of finding it for different functions.

Examples:
a) Let f(x) = 2x - 5; find f(x+h) - f(x)
b) Let f(x) = 3x + 2; find the difference quotient:
(f(x+h) - f(x))/h

The Difference Quotient
This video gives the formula for the difference quotient and do another example of finding it for a quadratic function.

Example:
Let f(x) = 2x2 - x + 5;
find and simplify the difference quotient
(f(x+h) - f(x))/h

Difference Quotient

Example:
Evaluate the difference quotient for f(x) = 4x2




Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
Mathway Calculator Widget



We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.