Difference Quotient Calculator

Use this difference quotient calculator to find how much a function changes on average over a specific interval. It displays stepwise calculations to measure the slope of the secant line which passes through two points.

What Is The Difference Quotient?

In calculus, a difference quotient is used to measure the slope of the secant line between the two different points on the graph of a function.

In simple words, the difference quotient measures the rate of change of a function f(x) for x in a given interval [x, x + h].

Difference Quotient Image:

Difference Quotient Formula:

The difference quotient equation measures the approximated form of the derivative as:

f(x) = f(x + h) – f(x) h

Where:

f(x) represents the function of “x”
h shows the interval size
x + h is the increment in the input

The difference quotient formula provides an approximation of a function's derivative.

How To Calculate Difference Quotient?

Follow these steps to determine difference quotients:

Identify the function: Determine the function f(x)
Evaluate f(x+h): Put (x+h) for x in the function f(x)
Find the difference: Subtract f(x) from f(x+h)
Divide by h: Divide the difference by h

Difference Quotient Examples:

Example #1:

Find the difference quotient for the following function:

F(x) = x² + 4

Solution:

To find f(x + h), put x + h instead of x:

f(x + h) = (x + h)² + 4

Then,

= ((x + h)² + 4) – (x² + 4) h

= h²+2hx + x² + 4 - x² - 4 h

= h²+2hx h

f(x) = x² + 4 = h + 2x

Thus, the difference quotient for f(x) = x^2 + 4 is h + 2x. For quick results, use our simplified difference quotient calculator.

Example #2:

Find the difference quotient of the function f(x) = 4x - 5.

Solution:

Using the difference quotient formula:

= f(x + h) - f(x) h

= (4(x + h) - 5) - (4x - 5) h

= 4x + 4h - 5 - 4x + 5 h

= 4h h

= 4

Determining the difference quotient for the f(x) = x^2 + 4 involves various steps. To simplify this kind of calculations, consider using the f(x+h)-f(x)/h calculator. No matter whether you are a beginner or a professional, our user-friendly difference quotient solver makes it easy to approximate the average rate of change of a given function.

References:

From the source of Wikipedia: Difference Quotient.

From the source of Cuemath: Difference Quotient Formula.