Using the definition of the derivative, find $f^{\text{'}}(x).$ Then find $f^{\text{'}}(1),f^{\text{'}}(2),$ and $f^{\text{'}}(3)$ when the derivative exists.

$f(x)=-x^2+2x-6$

To find the derivative, complete the limit as $h$ approaches $0$ for $\frac{f(x+h)-f(x)}{h}.$

$\underset{h0}{lim}$