Let $y=x^3-9x+4.$ Complete the steps below to compare $dy$ and $y.$

If needed, write your answer to at most $4$ decimal places.

$($a$)$ Find $x,y,$ and $dy$ as $x$ changes from $-3$ to $-3\mathrm{.}6.$

$x=y=$

$dy=$

$$

$($b$)$ Find $x,y,$ and $dy$ as $x$ changes from $-3$ to $-3\mathrm{.}2.$

$x=,dy=,dy=$

$$

$($c$)$ Looking at your answers for parts $($a$)$ and $($b$),$ as $x$ gets smaller, does the approximation $y$~~$dy$ become better? Choose the best answer.

Yes

No