Maharashtra State BoardHSC Commerce 11th
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Solve the following: The relation between price (P) and demand (D) of a cup of Tea is given by D = 12P. Find the rate at which the demand changes when the price is Rs. 2/-. Interpret the result. - Mathematics and Statistics

Sum

The relation between price (P) and demand (D) of a cup of Tea is given by D = `12/"P"`. Find the rate at which the demand changes when the price is Rs. 2/-. Interpret the result.

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Solution

Demand, D =`12/"P"`

Rate of change of demand = `("dD")/("dP")`

=`"d"/("dP")(12/"P")`

=`12"d"/("dP")("P"^-1)`

= `12((-1)"P"^-2)`

=`12((-1)/"P"^2)`

= `(-12)/"P"^2`

When price P = 2,
Rate of change of demand,`(("dD")/("dP"))_("P" = 2)`

= `(-12)/(2)^2`

= – 3
∴ When price is 2, Rate of change of demand is – 3
Here, rate of change of demand is negative
∴ demand would fall when the price becomes ₹ 2.

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 9 Differentiation
Miscellaneous Exercise 9 | Q III. (1) | Page 124
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