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Last updated date: 28th Nov 2023
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# In $y = 48x - 2{x^2}$,Where $y =$ total revenue in $\$ , $x = output$ ,At what output is the total revenue a maximum?A. $2$ B. $12$ C. $48$ D. $4$

Hint: The question is asking us to find the maximum value of the total revenue denoted in this case by $y$ , which corresponds to the value a company makes in dollar based on the value of output produced which here is denoted by $x$ , Thus we can say that $y$ is the function of $x$ . And we have to find the maxima of the function. When we find the maxima of the function we first put the derivative of the function equal to $0$ and then find the critical points, check the values of those points at the second derivative and if that value is negative the function is maxima at that critical point. The given function can be easily differentiated by the use of a standard formula.
$\Rightarrow y = 48x - 2{x^2} \\ \Rightarrow y' = 48 - 4x \;$
Upon putting $y'$ as $0$ we will get the value of critical points,
$\Rightarrow 0 = 48 - 4x$ ,
The critical point is therefore $12$ . This is the value of the output when the revenue of the company is maximum. The option B is therefore correct.