Question

Find the difference quotient of f; that is, find f(x+h)−f(x)/h, h≠0, for the following function.f(x)=3x+7

Answer 1

Solution:

Consider the following function:

$f(x)=3x+7$

then, the difference quotient of the given function is:

$\frac{f(x+h)-f(x)}{h}=\frac{(3(x+h)+7)-(3x+7)}{h}$

this is equivalent to:

$\frac{(3x+3h+7)-(3x+7)}{h}$

this is equivalent to:

$\frac{3x+3h+7-3x-7}{h}=\frac{(3x-3x)+3h+(7-7)}{h}$

this is equivalent to:

$\frac{3h}{h}=\text{ 3}$

so that, we can conclude that the correct answer is:

$3$