Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
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
संबंधित प्रश्न
Find the derivative of the following w. r. t.x.
`(3x^2 - 5)/(2x^3 - 4)`
Find the derivative of the following function by the first principle: `x sqrtx`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `2^x/logx`
Solve the following example: If the total cost function is given by; C = 5x3 + 2x2 + 7; find the average cost and the marginal cost when x = 4.
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.
The supply S for a commodity at price P is given by S = P2 + 9P − 2. Find the marginal supply when price is 7/-.
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y=(sqrtx+1)^2`
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
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.
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
Differentiate the following w.r.t.x :
y = `x^(4/3) + "e"^x - sinx`
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 = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
