Question

How do you use the limit definition of the derivative to find the derivative of `f(x)=2x+11`?

Answer 1

`f'(x)= 2`

Explanation:

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

so for `f(x)=2x+11` we have:
`f'(x)= lim_(h->0)({2(x+h)+11 - (2x+11)})/h`
`f'(x)= lim_(h->0)( 2x+2h+11 - 2x-11 )/h`
`f'(x)= lim_(h->0)( 2h )/h`
`f'(x)= lim_(h->0)( 2 )`
`f'(x)= 2`