Question

How do you use the definition of a derivative function to calculate f'(4) where `f(x) = x+3`?

Answer 1

The derivative of `f(x)`:
`f'(x) = lim_(hrarr0) (f(x+h)-f(x))/h`

For `f(x) = x+3`
`f'(x) = lim_(hrarr0)((x+h+3)-(x+3))/h`

`= lim_(hrarr0) h/h`

`=lim_(hrarr0)1`

`=1`

Note that `f'(x) = 1` for all values of `x`

So specifically
`f'(4) = 1`