Difference Quotient Calculator

Difference quotient of a function is the quotient value of change in the function value over change in the variable value.

Difference quotient is related to slope of a line drawn to a graph but its notation is slightly different compared to slope

equation. Difference quotient calculator is the online tool which can give a quick result for the difference quotient.



Example 1: Find the difference quotient of the function, f(x) = 5x + 3

Difference quotient = f(x+h) – f(x)
                                                  h


Given f(x) = 5x + 3   f(x + h) = 5(x + h) + 3

 f(x + h) = 5x + 5h + 3

Substituting in the above formula, we get

Difference quotient = (5x + 5h + 3) – (5x + 3)
                                                          h

 Difference quotient = (5x + 5h + 3 – 5x – 3)/ h   5h/h

 Difference quotient = 5 



Example 2: Find the difference quotient of the function, f(x) = 4x - 7

Difference quotient = f(x+h) – f(x)

                                                  h

Given f(x) = 4x – 7  f(x + h) = 4(x + h) - 7

 f(x + h) = 4x + 4h - 7

Substituting in the above formula, we get

 Difference quotient = (4x + 4h - 7) – (4x - 7)
                                                         h

 Difference quotient = (4x + 4h – 7 – 4x + 7)/ h  4h/h

 Difference quotient = 4