Advertisements
Advertisements
प्रश्न
If the total cost function is given by C = 5x3 + 2x2 + 1; Find the average cost and the marginal cost when x = 4.
Advertisements
उत्तर
Total cost function C = 5x3 + 2x2 + 1
Average cost = `"C"/x`
=`(5x^3 + 2x^2 + 1)/x`
= 5x2 + 2x +`1/x`
When x = 4, Average cost = 5(4)2 + 2(4) + `1/4`
= 80 + 8 + `1/4`
= `(320+32+1)/4`
= `353/4`
Marginal cost = `("dC")/("d"x)`
= `"d"/"d"x (5x^3 + 2x^2 + 1)`
=`5"d"/"d"(x^3) + 2"d"/"d"(x^2) + "d"/"d"(1)`
=5(3x2) + 2(2x) + 0
= 15x2 + 4x
When x = 4, marginal cost = `(("dC")/("d"x))_("x" = 4)`
= 15(4)2 + 4(4)
= 240 + 16
= 256
∴ The average cost and marginal cost at x = 4 are `353/4` and 256 respectively.
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 w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following function by the first principle: `x sqrtx`
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. : `x/log x`
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.
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/-.
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.
Differentiate the following function .w.r.t.x. : x5
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = "e"^x/logx`
Find `dy/dx`if y = x log x (x2 + 1)
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.
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)`
Select the correct answer from the given alternative:
If y = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
