Let $f(x) = 1 - 5 \sqrt{x}$. Then the expression $$\frac{f(x + h) - f(x)}{h}$$ can be written in the form $$\frac{A}{\left(\sqrt{Bx + Ch} \right) + \left(\sqrt{x} \right)},$$ where $A$, $B$, and $C$ are constants. (Note: It's possible for one or more of these constants to be 0.) Find the constants.

$A =$

$B =$

$C =$

Use your answer from above to find $\displaystyle{\lim_{h\rightarrow 0} \frac{f(x + h) - f(x)}{h}}$.

$\displaystyle{\lim_{h\rightarrow 0} \frac{f(x + h) - f(x)}{h}} =$

Finally, find each of the following:

$f'(1) =$

$f'(2) =$

$f'(3) =$