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. : `(x^2+a^2)/(x^2-a^2)`
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^x/logx`
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.
Differentiate the following function w.r.t.x. : x−2
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^3 – 2x^2 + sqrtx + 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`
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Differentiate the following w.r.t.x :
y = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
