Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given, P = 20 + D – D2
Rate of change of price = `("dP")/("dD")`
= `"d"/("dD") (20 + "D" - "D"^2)`
= 0 + 1 – 2D
= 1 – 2D
Rate of change of price at D = 3 is
`(("dP")/("dD"))_("D" = 3)`
= 1 – 2(3)
= – 5
∴ Price is changing at a rate of – 5 when demand is 3.
APPEARS IN
संबंधित प्रश्न
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. : `(3e^x-2)/(3e^x+2)`
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^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)`
Differentiate the following function w.r.t.x. : `2^x/logx`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
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.
The cost of producing x articles is given by C = x2 + 15x + 81. Find the average cost and marginal cost functions. Find marginal cost when x = 10. Find x for which the marginal cost equals the average cost.
Differentiate the following function .w.r.t.x. : x5
Differentiate the following function w.r.t.x. : x−2
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
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.
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
