Advertisements
Advertisements
Question
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.
Solution
Demand function, D =`sqrt(75 − 3"P")`
Now, Marginal demand = `("dD")/("dP")`
= `"d"/("dP")(sqrt(75 − 3"P"))`
=`1/(2 sqrt(75- 3"P")) *"d"/("dP") (75 - 3"P")`
=`1/(2 sqrt(75- 3"P"))*(0 - 3 xx1)`
=`(-3)/(2 sqrt(75 - 3"P"))`
When P = 5,
Marginal demand = `(("dD")/("dP")) _("P" = 5)`
=`(-3)/(2 sqrt(75 - 3(5)))`
= `(-3)/(2sqrt60)`
= `(-3)/(4sqrt15)`
∴ Marginal demand =`(-3)/(4sqrt15)` at P = 5.
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t.x. : `(x^2+a^2)/(x^2-a^2)`
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/log x`
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: 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: The demand function is given as P = 175 + 9D + 25D2 . Find the revenue, average revenue, and marginal revenue when demand is 10.
The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
Differentiate the following function .w.r.t.x. : x5
Differentiate the following function w.r.t.x. : x−2
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 = "e"^x/logx`
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
