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Difference Quotient Calculator

To use the Difference Quotient Calculator, enter the function, select the variable, and click calculate button

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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”.

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