Advertisements
Advertisements
Question
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
Solution
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
RELATED QUESTIONS
Find the derivative of the following w. r. t. x. : `logx/(x^3-5)`
Find the derivative of the following w. r. t. x. : `(xe^x)/(x+e^x)`
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 : `(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. : `((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 followingfunctions.w.r.t.x.: `1/sqrtx`
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 = x2 + 2x – 1
Find `dy/dx` if y = (1 – x) (2 – x)
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^(7/3) + 5x^(4/5) - 5/(x^(2/5))`
