Difference quotient is the term used in calculus to determine the abstracts of slopes and average rate change. If in a graph there are two points through which the slope passes for which the graph of function f is determined. These points are of x-coordinates x and x+h.

The Difference quotient formula for the function f is given by,

$f$ = $\frac{f(x+h) - f(x)}{h}$.

The difference quotient  gives the derivative of the function.


Let's see some examples on Difference quotient:

Question 1: Calculate the difference quotient for the function f(x) = 3x + 2 for h = 2.
Solution:

Given: The function is f(x) = 3x + 2

f(x+h) = f(x+2) = 3(x+2) + 2 = 3x + 8

The Difference quotient formula for the function f is given by,
f = $\frac{f(x+h) - f(x)}{h}$

f = $\frac{(3x+8) - (3x+2)}{2}$

f = $\frac{6}{2}$

f = 3

Question 2: Calculate the difference quotient for the function f(x) = x$^{2}$ + 2 for h = 3.
Solution:

Given: The function is f(x) = x$^{2}$ + 2

f(x+h) = f(x+3) = (x+3)$^{2}$ + 2 = x$^{2}$+ 6x + 9 + 2 = x$^{2}$ + 6x + 11

The Difference quotient formula for the function f is given by,
f = $\frac{f(x+h) - f(x)}{h}$

f = $\frac{(x^2 + 6x + 11) - (x^2 + 6x + 9)}{3}$
 
f = $\frac{2}{3}$.