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Home  >>  CBSE XII  >>  Math  >>  Application of Derivatives
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The total revenue in Rupees received from the sale of \(x\) units of a product is given by $ R(x) = 13x^2 + 26x + 15.$ Find the marginal revenue when \(x = 7\).

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1 Answer

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Toolbox:
  • 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 $x=x_0$
  • Marginal revenue is the rate of change of total revenue w.r.t the number of units sold.
Step 1:
Since the marginal revenue is the rate of change of total revenue w.r.t the number of units sold.
Marginal revenue (MR)=$\large\frac{dR}{dx}$
$\qquad\qquad\qquad\qquad=\large\frac{d}{dx}$$\big(13x^2+26x+15)$
Step 2:
On differentiating we get,
$\large\frac{dR}{dx}$$=26x+26$
The marginal revenue when $x=7$
$\large\frac{dR}{dx}=$$26\times 7+26$
$\qquad=Rs.208$
answered Jul 8, 2013 by sreemathi.v
 

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