Question:
The total revenue in Rupees received from the sale of \(x\) units of a product is given by \(R(x)=3x^2+36x+5\).The marginal revenue, when \(x=15\) is
The total revenue in Rupees received from the sale of \(x\) units of a product is given by \(R(x)=3x^2+36x+5\).The marginal revenue, when \(x=15\) is
Updated On: Sep 12, 2023
116
96
90
126
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The Correct Option is D
Solution and Explanation
The correct answer D:Rs 126
Marginal revenue is the rate of change of total revenue with respect to the number of units sold.
\(∴Marginal\space Revenue (MR)=\frac{dR}{dx}=3(2x)+36=6x+36\)
\(∴When\space x = 15,\)
\(MR = 6(15) + 36 = 90 + 36 = 126\)
Hence, the required marginal revenue is Rs 126.
Marginal revenue is the rate of change of total revenue with respect to the number of units sold.
\(∴Marginal\space Revenue (MR)=\frac{dR}{dx}=3(2x)+36=6x+36\)
\(∴When\space x = 15,\)
\(MR = 6(15) + 36 = 90 + 36 = 126\)
Hence, the required marginal revenue is Rs 126.
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Concepts Used:
Application of Derivatives
Various Applications of Derivatives-
Rate of Change of Quantities:
If some other quantity ‘y’ causes some change in a quantity of surely ‘x’, in view of the fact that an equation of the form y = f(x) gets consistently pleased, i.e, ‘y’ is a function of ‘x’ then the rate of change of ‘y’ related to ‘x’ is to be given by
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This is also known to be as the Average Rate of Change.
Increasing and Decreasing Function:
Consider y = f(x) be a differentiable function (whose derivative exists at all points in the domain) in an interval x = (a,b).
- If for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) ≤ f(x2); then the function f(x) is known as increasing in this interval.
- Likewise, if for any two points x1 and x2 in the interval x such a manner that x1 < x2, there holds an inequality f(x1) ≥ f(x2); then the function f(x) is known as decreasing in this interval.
- The functions are commonly known as strictly increasing or decreasing functions, given the inequalities are strict: f(x1) < f(x2) for strictly increasing and f(x1) > f(x2) for strictly decreasing.
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