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. : `logx/(x^3-5)`
Find the derivative of the following w. r. t.x. : `(3e^x-2)/(3e^x+2)`
Find the derivative of the following function by the first principle: 3x2 + 4
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x. : `x/log x`
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 supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
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. : `xsqrt x`
Differentiate the followingfunctions.w.r.t.x.: `1/sqrtx`
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx` if y = x2 + 2x – 1
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx if y = ((logx+1))/x`
Find `dy/dx if y = "e"^x/logx`
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.
Differentiate the following w.r.t.x :
y = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`
