The total revenue (in Rs.) received from the sale of x units of a product is given by \(R(x) = 2x^2 + 25x + 40\). The marginal revenue when \(x = 6\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs. 49
The marginal revenue is the rate of change of total revenue with respect to the number of units sold:
\( \displaystyle MR = \frac{dR}{dx} \)
\( = 4x + 25 \)
At x = 6:
\(MR = 24 + 25 = 49\)
So the marginal revenue is Rs. 49.
Why the other options are incorrect
Option (1) Rs. 37 — Incorrect. This uses 2x + 25 as the derivative; the derivative of \(2x^2\) is 4x.
Option (3) Rs. 262 — Incorrect. This is R(6) = 72 + 150 + 40, the total revenue, not the marginal revenue.
Option (4) Rs. 24 — Incorrect. This is only the term 4x at x = 6; the constant 25 from 25x is left out.