Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Total cost function, C = 5x3 + 2x2 + 7
Average cost = `"C"/x`
=`(5x^3 + 2x^2 + 7)/x`
= 5x2 + 2x + `7/x`
When x = 4,
Average cost = 5(4)2 + 2(4) + `7/4`
= 80 + 8 + `7/4`
= `(320 + 32+ 7)/4`
= `359/4`
Marginal cost = `("dC")/("d"x)`
=`"d"/("d"x)(5x^3 + 2x^2 + 7)`
= `5"d"/("d"x) (x^3) + 2"d"/("d"x)(x^2) + "d"/("d"x)(7)`
= 5(3x2) + 2(2x) + 0
= 15x2 + 4x
When x = 4, Marginal cost = `(("dC")/"dx")_ (x = 4)`
= 15(4)2 + 4(4)
= 240 + 16
= 256
∴ the average cost and marginal cost at x = 4 are `359/4` and 256 respectively.
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. : `(3e^x-2)/(3e^x+2)`
Find the derivative of the following function by the first principle: 3x2 + 4
Differentiate the following function w.r.t.x. : `1/("e"^x + 1)`
Differentiate the following function w.r.t.x. : `x/log x`
Differentiate the following function w.r.t.x. : `2^x/logx`
If for a commodity; the price-demand relation is given as D =`("P"+ 5)/("P" - 1)`. Find the marginal demand when price is 2.
The demand function of a commodity is given as P = 20 + D − D2. Find the rate at which price is changing when demand is 3.
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
Find `dy/dx if y = x^2 + 1/x^2`
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^(4/3) + "e"^x - sinx`
Select the correct answer from the given alternative:
If y = `(x - 4)/(sqrtx + 2)`, then `("d"y)/("d"x)`
