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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 \(x = 7\).
cbse
class12
bookproblem
ch6
sec1
q16
p198
sec-a
easy
math
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asked
Nov 23, 2012
by
thanvigandhi_1
edited
Jul 8, 2013
by
sreemathi.v
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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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