The total revenue in Rupees received from the sale of x units of a product is given by R ( x ) = 3 x 2 + 36x + 5 . The marginal revenue, when x = 15 is (A) 116 (B) 96 (C) 90 (D) 126

Option D is correct We have, R(x) = 3 x 2 + 36x + 5 …(i) Differentiating (i) w.r.t. x , we get, marginal revenue dx = dx (3 x 2 + 36x + 5) = 6x + 36 = ( dx ) x = 15 = 6 15 + 36 = 126 [couleur = blue!30, arrondi = 0.1 ] NCERT - Exercise – 6.2

Application of Derivatives — Class 12 Maths Solution

ncert exercise SA NCERT Ex.6.1,Q.No. 18,Page 198

Question

The total revenue in Rupees received from the sale of $x$ units of a product is given by$R\left( x \right) = 3{x^2} + 36x + 5$. The marginal revenue, when $x = 15$ is

(A) $116$

(B) $96$

(D) $126$

Step-by-step Solution

Option D is correct

We have, $R(x) = 3{x^2} + 36x + 5$ …(i)

Differentiating (i) w.r.t. $x$, we get,

marginal revenue $\cfrac{{dR}}{{dx}} = \cfrac{d}{{dx}}(3{x^2} + 36x + 5) = 6x + 36$
$= {\left( {\cfrac{{dR}}{{dx}}} \right)_{x = 15}} = 6 \times 15 + 36 = 126$

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