Given the function f(x)= 4+4x^2, calculate the following values:

Question

[f(a+h)-f(a)]/h

Answer 1

You will have to pick a value of a and of h. If you want a general expression for
[f(a+h)-f(a)]/h with that function, it would be
[4(a+h)^2 - 4a^2]/h
= (8ah +h^2)/h
= 8a +4h

Note that it approaches a constant 8a when h->0
That is called the derivative of the function at a.