Question

How do you find f'(x) using the definition of a derivative for `f(x)= 5x + 9` at x=2?

Answer 1

See the explanation.

Explanation:

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

`f'(x)=lim_(h->0) (5(x+h)+9-(5x+9))/h`

`f'(x)=lim_(h->0) (5x+5h+9-5x-9)/h`

`f'(x)=lim_(h->0) (5h)/h=lim_(h->0) 5 = 5`

`f'(x)=5`