The revenue (in lakh rupees) from selling a product is given by

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The revenue

R

(in lakh rupees) from selling a product is given by

R(p) = 120p - 10p^{2}

, where

p

(in rupees) is the selling price per unit. The price is increasing with time

t

(in months) at the rate

\dfrac{dp}{dt} = 0.5\,\text{rupee/month}

when

p = 6

. (i) Find

\dfrac{dR}{dt}

at that time. (ii) Calculate the percentage rate of change of revenue at that time, correct to two decimal places.