Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Total cost of ‘t’ toy cars, C = 5(2t) + 17
Marginal Cost =`("dC")/"dt"`
= `d/dt [5(2^t) + 17]`
=`5"d"/"dt"(2^"t")+"d"/"dt"(17)`
= 5(2t . log 2) + 0
= 5(2t . log 2)
When t = 3,
Marginal cost =` (("dC")/("dt"))_("t" = 3)`
= 5(23. log 2)
= 40 log 2
Average cost =`"C"/"t"= (5(2)^"t"+17)/t`
When t = 3, averagecos = `(5(2^3) + 17)/3`
= `(40+ 17)/3` = 19
∴ at t = 3, Marginal cost is 40 log 2 and Average cost is 19.
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)`
Find the derivative of the following function by the first principle: 3x2 + 4
Find the derivative of the following function by the first principle: `x sqrtx`
Differentiate the following function w.r.t.x. : `((2"e"^x - 1))/((2"e"^x + 1))`
Differentiate the following function w.r.t.x. : `((x+1)(x-1))/(("e"^x+1))`
Solve the following example: The total cost of producing x units is given by C = 10e2x, find its marginal cost and average cost when x = 2.
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. : x−2
Differentiate the following function w.r.t.x. : `xsqrt x`
Find `dy/dx if y=(sqrtx+1)^2`
Find `dy/dx if y=(1+x)/(2+x)`
Find `dy/dx if y = ((logx+1))/x`
The demand (D) of biscuits at price P is given by D = `64/"P"^3`, find the marginal demand when price is Rs. 4/-.
Differentiate the following w.r.t.x :
y = `x^(4/3) + "e"^x - sinx`
Differentiate the following w.r.t.x :
y = `x^(7/3) + 5x^(4/5) - 5/(x^(2/5))`
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)` =
