Advertisements
Advertisements
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.
Advertisements
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.
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
Find the derivative of the following w. r. t.x.
`(3x^2 - 5)/(2x^3 - 4)`
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
The demand function of a commodity is given as P = 20 + D − D2. Find the rate at which price is changing when demand is 3.
Solve the following example: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.
Solve the following example: The total cost function of producing n notebooks is given by C= 1500 − 75n + 2n2 + `"n"^3/5`. Find the marginal cost at n = 10.
Solve the following example: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
The demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
The supply S of electric bulbs at price P is given by S = 2P3 + 5. Find the marginal supply when the price is ₹ 5/- Interpret the result.
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
Differentiate the following w.r.t.x :
y = `x^(4/3) + "e"^x - sinx`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
