Question

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/-.

Answer 1

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.