Question

How do you find the derivative of `f(x)=3x+2` using the limit process?

Answer 1

`f'(x)=3`

Explanation:

Recall that the derivative of any function `f(x)` is given by:

`f'(x)=lim_(h->0)` `((f(x+h)-f(x))/h)`

Let `f(x)=3x-2`

`f'(x)=lim_(h->0)` `((3(x+h)-2-(3x-2))/h)`

`=lim_(h->0)` `((3x+3h-2-3x+2)/h)`

`=lim_(h->0)` `((3h)/h)`

`=lim_(h->0)` `(3)=3`