Consider the revenue function $R(x)=2x$ and the cost function $C(x)=\sqrt{8x+32}$. Determine all break-even points.
Antwoord 1 correct
Correct
Antwoord 2 optie
$x=-2$
Antwoord 2 correct
Fout
Antwoord 3 optie
$x=-2$ and $x=4$
Antwoord 3 correct
Fout
Antwoord 4 optie
$x=0$
Antwoord 4 correct
Fout
Antwoord 1 optie
$x=4$
Antwoord 1 feedback
Correct:
$$\begin{align*}
R(x) = C(x) & \Leftrightarrow 2x=\sqrt{8x+32}\
& \Rightarrow (2x)^2=8x+32\\
& \Leftrightarrow 4x^2=8x+32\\
& \Leftrightarrow 4x^2-8x-32=0\\
& \Leftrightarrow x^2-2x-8=0\\
& \Leftrightarrow (x-4)(x+2)=0\\
& \Leftrightarrow x=4 \mbox{ or } x=-2.
\end{align*}$$
Note that $x=-2$ is no solution of $R(x)=C(x)$. Hence, the break-even point is $x=4$.
Go on.
$$\begin{align*}
R(x) = C(x) & \Leftrightarrow 2x=\sqrt{8x+32}\
& \Rightarrow (2x)^2=8x+32\\
& \Leftrightarrow 4x^2=8x+32\\
& \Leftrightarrow 4x^2-8x-32=0\\
& \Leftrightarrow x^2-2x-8=0\\
& \Leftrightarrow (x-4)(x+2)=0\\
& \Leftrightarrow x=4 \mbox{ or } x=-2.
\end{align*}$$
Note that $x=-2$ is no solution of $R(x)=C(x)$. Hence, the break-even point is $x=4$.
Go on.
Antwoord 2 feedback
Antwoord 3 feedback
Antwoord 4 feedback