Let $y=x^3-4x+1.$ 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 $2$ to $2\mathrm{.}5.$

$x=$

$$

$y=$

$$

$dy=$

$$

$($b$)$ Find $x,y,$ and $dy$ as $x$ changes from $2$ to $2\mathrm{.}1.$

$x=$

$$

$y=$

$$

$dy=$

$$

$($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