Question

1. Consider f(x) = 3x - 5

Find f(x+h)-f(x)/ h
(Difference Quotient) please show work and answer.​

Answer 1

3

Explanation:

Here we have the function

`f(x)=3x-5`

We want to find the following ratio:

`(f(x+h)-f(x))/(h)`

Note that the limit of this for
`h\rightarrow 0` is equivalent to the derivative of the function.

Here we have:

`f(x+h)=3(x+h)-5=3x+3h-5`

And

`f(x)=3x-5`

Therefore we have

`f(x+h)-f(x)=3x+3h-5-(3x-5)=3h`

And therefore,

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