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