How do I solve this derivative related problem?

Question

Let f(x) = -2 - x^2. Find the following:

f(3 + h) - f(3)
-------------
h

Been working on it a while and can't seem to get rid of some pesky things. Thanks much.

Answer 1

[f(3 + h) - f(3)]/h = [-2 - (3 + h)^2 - (-2 - 3^2)]/h =
[-2 - (9 + 6h + h^2) + 2 + 9]/h = -(6h + h^2)/h = -(6 + h).

Answer 2

You're looking for the derivative when evaluated at the point x = 3

The derivative of -2 - x^2 is -2x
Evaluated at x = 3, this is -6.