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

Consider the following function:

`f(x)=3x+7`

then, the difference quotient of the given function is:

`(f(x+h)-f(x))/(h)=((3(x+h)+7)-(3x+7))/(h)`

this is equivalent to:

`((3x+3h+7)-(3x+7))/(h)`

this is equivalent to:

`(3x+3h+7-3x-7)/(h)=((3x-3x)+3h+(7-7))/(h)`

this is equivalent to:

`(3h)/(h)=\text{ 3}`

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

`3`