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Question
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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