Advertisements
Advertisements
Question
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.
Solution
Given, cost C = x2 + 15x + 81
Average cost = `"C"/x=(x^2+15x+81)/x`
= x + 15 + `81/x`
and Marginal cost = `("dC")/("d"x)`
= `"d"/("d"x)(x^2 + 15x + 81)`
= `"d"/("d"x)(x^2) + 15d/("d"x)(x) + "d"/("d"x)(81)`
= 2x + 15(1) + 0
= 2x + 15
When x = 10,
Marginal cost = `(("dC")/("d"x))_(x = 10)`
= 2(10) + 15
= 35
If marginal cost = average cost, then
2x + 15 = x + 15 + `81/x`
∴ x = `81/x`
∴ x2 = 81
∴ x = 9 …[∵ x > 0]
APPEARS IN
RELATED QUESTIONS
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following function by the first principle: 3x2 + 4
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. : `2^x/logx`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
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.
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: If for a commodity; the demand function is given by, D = `sqrt(75 − 3"P")`. Find the marginal demand function when P = 5.
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^2 + 1/x^2`
Find `dy/dx` if y = (1 – x) (2 – x)
The relation between price (P) and demand (D) of a cup of Tea is given by D = `12/"P"`. Find the rate at which the demand changes when the price is Rs. 2/-. Interpret the result.
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`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
