A fruit warehouse has weekly sales $\backslash ($ y $\backslash ),$ in thousands of pound sold that depends on the price $\backslash ((\backslash$mathrm$\{$p$\})\backslash )$ in dollars per pound. Find the rate of change of weekly sales with respect to price.

$\backslash [$

y$=32(3$ p$+4)^\{-\backslash$frac$\{2\}\{3\}\}$

$\backslash ]$

$\backslash ($ y$^\{\backslash$prime$\}=\backslash )$

What is the rate of change of weekly sales, rounded to $2$ decimal places, with respect to price when the price is $2\mathrm{.}63?$

thousands of pounds

Use Marginal Analysis to approximate the change in the weekly sales if the price changes from $2\mathrm{.}63$ to $2\mathrm{.}27$ : thousands of pounds.