# 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.

#### 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