## Related questions with answers

Use Dell's recommendation feature to select a laptop computer (hint: visit Dell website, select "small and medium business," then click on "laptop"). What decision rule or combination of rules does this decision aid reflect? What type of consumer would be most likely to utilize this adviser function?

After a great deal of experimentation, two Atlantic Institute of Technology senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked, its cork travels according to

$s(t)=-16 t^2+40 t+3,$

where s is its height (in feet) above the ground t seconds after being released. (a) How high will it go? (b) How long is it in the air?

Solution

VerifiedGiven:

$\begin{align*} s(t)&=-16t^2+40t+3 \\t&\geq 0 \end{align*}$

(a) $\textbf{Critical numbers}$

Determine the derivative of the given function using $\frac{d}{dx}x^n=nx^{n-1}$:

$\begin{align*} s'(t)&=-16(2t)+40=-32t+40 \end{align*}$

Determine the roots of the derivative:

$\begin{align*} s'(t)&=0 \\ -32t+40&=0 &\color{#4257b2}\text{Substitute} \\ -32t&=-40 &\color{#4257b2}\text{Subtract 40 from each side} \\ t&=\frac{40}{32} &\color{#4257b2}\text{Divide each side by $-32$} \\ t&=\frac{5}{4}=1.25 &\color{#4257b2}\text{Evaluate} \end{align*}$

Next, the critical numbers are all values in the domain of the function for which the derivative is 0 or the derivative doesn't exist.

$\begin{align*} \text{Critical numbers: }t=\frac{5}{4}=1.25 \end{align*}$

## Create an account to view solutions

## Create an account to view solutions

## More related questions

- business math

1/4

- business math

1/7