Objective $[1\mathrm{.}6]$

Let $f(x)=8\mathrm{.}2x^2-4\mathrm{.}5x$

Using the difference quotient, $\frac{f(xh)-f(x)}{h}$ find ever better estimates of the derivative of $f^{\text{'}}(6)$

for the following values of $h$ :

$($enter values for $f^{\text{'}}(6)$ to nearest $0\mathrm{.}0001$ if necessary$)$

$h=0\mathrm{.}1$:$,m=$

$h=0\mathrm{.}01$:$,m=$

$h=0\mathrm{.}001$:$,m=$

$$

$$

$$

Consider the function $g(x)=\sqrt[\phantom{2}]{3x6}.$ Fill in the missing information in the table below. $($Round your answers of least $3$ decimal places.$)$

$\backslash$table$[[b,\frac{g(b)-g(3)}{b-3}$