$(A)\; 116 \qquad (B)\; 96 \qquad (C)\; 90 \qquad (D)\; 126 $

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- If $y=f(x)$,then $\large\frac{dy}{dx}$ measures the rate of change of $y$ w.r.t $x$.
- $\big(\large\frac{dy}{dx}\big)_{x=x_0}$ represents the rate of change of $y$ w.r.t $x$ at $x=x_0$

Step 1:

Since the marginal revenue is the rate of change of total revenue w.r.t the number of units sold.

Given : $R(x)=3x^2+36x+5$

Therefore $\large\frac{dR}{dx}=\frac{d}{dx}$$(3x^2+36x+5)$

$\qquad\qquad\;\;\;\;=6x+36$

Step 2:

When $x=15$

$\large\frac{dR}{dx}$$=6\times 15+36$

$\quad\;\;=Rs.126$

Hence $D$ is the correct option.

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