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The demand D for a price P is given as D = 27P, find the rate of change of demand when price is Rs. 3/-. - Mathematics and Statistics

Sum

The demand D for a price P is given as D = `27/"P"`, find the rate of change of demand when price is Rs. 3/-.

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Solution

Demand, D = `27/"P"`

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

=`"d"/("dP")(27/"P")`

=`27"d"/"dP"(1/"P")`

=`27"d"/("dP")(1/"P")`

=`27"d"/("dP")("P"^-1)`

=27((-1)P-2)

=`27((-1)/"P"^2)=(-27)/"P"^2`

When price P = 3,
Rate of change of demand,

`(("dD")/("dP"))_("p" = 3) = (-27)/(3)^2= -3`

∴ When price is 3, Rate of change of demand is – 3.

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APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 9 Differentiation
Exercise 9.2 | Q II. (1) | Page 122
Balbharati Mathematics and Statistics 1 (Commerce) 11th Standard Maharashtra State Board
Chapter 9 Differentiation
Miscellaneous Exercise 9 | Q III. (5) | Page 124
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