Advertisements
Advertisements
Question
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
Solution
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.
RELATED QUESTIONS
Find the derivative of the following functions by the first principle: `1/(2x + 3)`
Differentiate the following function w.r.t.x : `(x^2 + 1)/x`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `x/log x`
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 demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
Differentiate the following function .w.r.t.x. : x5
Find `dy/dx if y=(sqrtx+1)^2`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx` if y = (1 – x) (2 – x)
Find `dy/dx if y=(1+x)/(2+x)`
Find `dy/dx if y = "e"^x/logx`
Differentiate the following w.r.t.x :
y = `x^(4/3) + "e"^x - sinx`
Differentiate the following w.r.t.x :
y = `sqrt(x) + tan x - x^3`
Differentiate the following w.r.t.x :
y = `7^x + x^7 - 2/3 xsqrt(x) - logx + 7^7`
Differentiate the following w.r.t.x :
y = `3 cotx - 5"e"^x + 3logx - 4/(x^(3/4))`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
