Difference Quotient Examples

Difference quotient is used to find the slope of the secant line in a graph of function f. Refer the below difference quotient examples to find the slope for the curved line provided between the two points in a graph of a function 'f'.

Example 1:

Let us consider the problem: Find the difference quotient for the function : 3x + 6x + 5

Solution:

We can calculate the difference quotient using the given formula.

Formula :

Difference quotient = (f(x + h) - f(x)) / h

Substituting the values in the formula,

Step 1 :

f(x+h) = 9(x+h) + 5

Step 2 :

f(x) = 9x+5

Step 3 :

9(x+h) + 5 - (9x+5)
=9x + 9h + 5 - 9x - 5
= 9h

Step 4 :

9h / h = 9
Hence 9 is the difference quotient.

Example 2:

Let us consider the difference quotient example problem: Find the difference quotient for the equation: 8x + 4

Solution:

Substituting the values in the formula,

Step 1 :

f(x+h) = 8(x+h) + 4

Step 2 :

f(x) = 8x+4

Step 3 :

8(x+h) + 4 - (8x+4)
=8x + 8h + 4 - 8x - 4
= 8h

Step 4 :

8h / h = 8
Hence 8 is the difference quotient.

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