Your Result is copied!

ADVERTISEMENT

Enter the function, choose the variable, and click on the “Calculate” button to calculate the difference quotient.

Add this calculator to your site

ADVERTISEMENT

ADVERTISEMENT

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.

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].

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.

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

**Example #1:**

Find the difference quotient for the following function:

F(x) = x^{2} + 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) – (x^{2} + 4) h

= h^{2}+2hx + x^{2} + 4 - x^{2} - 4 h

= h^{2}+2hx h

f(x) = x^{2} + 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.

**Support**

**Email us at**

© Copyrights 2024 by Calculator-Online.net