If f(x)=x^2+2 then f(x+h)=???

Answer 1

(x+h)^2 + 2

= x^2 + 2 x h + h^2 + 2

the are getting you ready to find the derivative
which is the limit as h -->0
of
[f(x+h) - f(x) ]/h
which here would be
limit as h -->0 of
(2 x h + h^2)/h
or
2 x + h
as h -->0
is
2x
which is df(x)/dx