Question

$y=48x-2x^2$
where, $y=$ Total revenue $.$x = $ Output
At what output is total revenue a maximum?

• A. $2$
• B. $12$
• C. $48$
• D. $4$

Answer 1

Answer: (B)

$12$

$\Rightarrow$ We have given, $y=48x-2x^2$

$\Rightarrow$ Differentiate on both sides w.r.t $x$ we get,

$\Rightarrow$ $\frac{dy}{dx}=48-4x$ --- ( 1 )

$\Rightarrow$ Let $\frac{dy}{dx}=0$

$\Rightarrow$ $48-4x=0$

$\Rightarrow$ $4x=48$

$\Rightarrow$ $x=12$ is a turning point.

$\Rightarrow$ $\frac{d^{2}y}{d{x}^2}=-4$ [Differentiate ( 1 ) on both sides]

$\Rightarrow$ So, the turning point is a maximum