Advertisements
Advertisements
प्रश्न
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
उत्तर
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
संबंधित प्रश्न
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following functions by the first principle: `1/(2x + 3)`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
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 ‘t’ toy cars is given by C=5(2t)+17. Find the marginal cost and average cost at t = 3.
Solve the following example: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
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 = x2 + 2x – 1
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx`if y = x log x (x2 + 1)
The demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
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`
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
