Question

Question #ae316

Answer 1

See the explanation below.

Explanation:

`f(x)=x^2 + 3`

(Note that `f(x+h) = (x+h)^2+3 = x^2+2xh+h^2+3`)

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

`= lim_(hrarr0)(((x+h)^2+3)-(x^2+3))/h` `" "` (form `0/0`)

`= lim_(hrarr0)(x^2+2xh+h^2+3-x^2-3)/h` `" "` (form `0/0`)

`= lim_(hrarr0)(2xh+h^2)/h` `" "` (form `0/0`)

`= lim_(hrarr0)(h(2x+h))/h` `" "` (form `0/0`)

`= lim_(hrarr0)(2x+h) = 2x`

So `f'(x) = 2x`