Consider the function $f(x) = 4x-x^{2}$.

Use the limit definition to compute the following derivative values:
$f'(0) =$
$f'(1) =$
$f'(2) =$
$f'(3) =$

Conjecture a formula for $f'(a)$ that depends only on the value $a$. That is, in the same way that we have a formula for $f(x)$ (recall $f(x) = 4x-x^{2}$), see if you can use your work above to guess a formula for $f'(a)$ in terms of $a$.
$f'(a) =$