Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Total cost function,
C = 1500 − 75n + 2n2 + `"n"^3/5`
Marginal Cost = `("dC")/("dn")`
=`"d"/("dn")(1500 - 75"n" + 2"n"^2 + "n"^3/5)`
=`d/(dn)(1500) - 75"d"/("dn")("n")+2"d"/("dn")("n"^2) + 1/5"d"/("dn")("n"^3)`
= `0 - 75(1) + 2(2"n")+1/5(3"n"^2)`
= `-75 + 4"n" + (3"n"^2)/5`
When n = 10,
Marginal cost
=`(("dC")/("dn"))_("n" = 10)`
= `-75 + 4(10) + 3/5 (10)^2`
= –75 + 40 + 60
= 25
∴ Marginal cost at n = 10 is 25.
APPEARS IN
संबंधित प्रश्न
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.
`(3x^2 - 5)/(2x^3 - 4)`
Differentiate the following function w.r.t.x. : `x/(x + 1)`
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `"e"^x/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `2^x/logx`
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 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.
Find `dy/dx if y = x^2 + 1/x^2`
Find `dy/dx if y = (sqrtx + 1/sqrtx)^2`
Find `dy/dx if y = x^3 – 2x^2 + sqrtx + 1`
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 = `x^(4/3) + "e"^x - sinx`
Differentiate the following w.r.t.x :
y = `log x - "cosec" x + 5^x - 3/(x^(3/2))`
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 = `(3x + 5)/(4x + 5)`, then `("d"y)/("d"x)` =
