Question $5.$ Let $f(x)=64x4x^2.$ If $h0,$ then the difference quotient can be simplified as

$\frac{f(xh)-f(x)}{h}=AhBxC$

where $A,B,$ and $C$ are constants. $($Note: It is possible for one or more of these constants to be $0.)$

$($a$)$ Simplify the difference quotient to find the constants $A,B,$ and $C.$

$($b$)$ Use the simplified expression, found in part $($a$),$ to find $f^{\text{'}}(x)=\underset{h0}{lim}\frac{f(xh)-f(x)}{h}.$

$($c$)$ Find each of the following values.

i$.f^{\text{'}}(1)$

ii$.f^{\text{'}}(2)$

iii. $f^{\text{'}}(3)$