Difference Quotient Calculator

Difference Quotient Calculator

Difference quotient calculator is used to calculate the rate of change of the given function. This difference quotient calculator provides a step-by-step solution for every reliable input.

What is the Difference quotient?

In mathematics, the term “difference quotient” refers to an expression that represents the average rate of change of a function over a small interval. It is usual practice in calculus to approximate the derivative of a function, which denotes the instantaneous rate of change of a function at a specific position.

It is denoted by “h” or “Ꙙx” and its mathematical formula is represented as.

Ꙙx = (f(x + h) - f(x)) / h

Where,

• f(x) = function of “x” 
• h = interval size 
• x + h = small increment in the input.

How to calculate the difference quotient?

Here are a few examples to learn how to evaluate difference quotient.

Example 1

If f(x) = 3y2-2x then calculate the difference quotient.

Solution

Step 1: Take the given function.

f(x) = −2x+3y2

Step 2: Write the formula of the Difference Quotient.

Ꙙx = (f(x + h) - f(x)) / h

Step 3: Now, put “x = x + h” in f(x).

f(x+h)= −2(x + h) + 3y²

f(x+h)= −2x - 2h + 3y2

Step 4: Put the values f(x) and f(x+h) in the formula.

Ꙙx =[−2x - 2h + 3y²] - [−2x+3y²]/ h

Ꙙx = −2x - 2h + 3y² + 2x - 3y²/ h

Ꙙx = - 2h/ h

Ꙙx = - 2

Hence, Ꙙx = - 2, the difference quotient of “f(x) = 3y²-2x”.

Example 2

If f(x) = 3x + 1 then calculate the difference quotient.

Solution

Step 1: Take the given function.

f(x) = 3x + 1

Step 2: Write the formula of the Difference Quotient.

Ꙙx = (f(x + h) - f(x)) / h

Step 3: Now, put “x = x + h” in f(x).

f(x+h)= 3(x + h) + 1

f(x+h)= 3x + 3h + 1

Step 4: Put the values f(x) and f(x+h) in the formula.

Ꙙx =[3x + 3h + 1] - [3x + 1]/ h

Ꙙx = 3x + 3h + 1 - 3x - 1/ h

Ꙙx = 3h/ h

Ꙙx = 3

Hence, Ꙙx =  3, the difference quotient of “f(x) = 3x + 1”.