# Difference Quotient Calculator

Difference Quotient Calculator calculates the difference quotient for the given function. The difference quotient formula gives the slope of a secant line that is drawn to a curve.

## What is a Difference Quotient Calculator?

Difference Quotient Calculator is an online tool that helps to calculate the difference quotient for the given function. This online difference quotient calculator helps you to calculate the difference quotient in a few seconds. To use this difference quotient calculator, enter the function in the given input box.

## How to Use Difference Quotient Calculator?

Please follow the steps below to find the difference quotient using an online difference quotient calculator:

**Step 1:**Go to Cuemath’s online difference quotient calculator.**Step 2:**Enter the function in the given input box of the difference quotient calculator.**Step 3:**Click on the**"Calculate"**button to calculate the difference quotient for the given function.**Step 4:**Click on the**"Reset"**button to clear the field and enter a new function.

## How does Difference Quotient Calculator work?

Let us consider a curve y = f(x) and a secant line that passes through two points of the curve (x, f(x)) and (x + h, f(x + h)). The formula to calculate the difference

the quotient is given by \(\dfrac{f(x+h)-f(x)}{h}\)

Note:** **As h → 0, the secant of y = f(x) becomes a tangent to the curve y = f(x). Thus, as h → 0, the difference quotient gives the slope of the tangent and hence it

gives the derivative of y = f(x). i.e., \(\lim_{x \rightarrow 0} \dfrac{f(x+h)-f(x)}{h}\)

Let us understand this with the help of the following example.

**Solved Example on Difference Quotient**

Find the difference quotient for f(x) = 2x + 5 and verify it using the difference quotient calculator?

**Solution**:

Given: f(x) = 2x + 5

f(x + h) = 2(x + h) + 5

= 2x + 2h + 5

Difference quotient = \(\dfrac{f(x+h)-f(x)}{h}\)

= 2x + 2h + 5 - 2x - 5 / h

= 2h / h

= 2

Now, try the difference quotient calculator and find the difference quotient for:

- f(x) = 5x + 7
- f(x) = - 4x + 9