Given the total cost function for x units of a commodity as C ( x ) = 1 3 x 3 + x 2 - 8 x + 5 , find the marginal cost function.

Given, cost function C ( x ) = 1 3 x 3 + x 2 - 8 x + 5 Marginal cost is rate of change of cost. Marginal cost function M C = d d x ( 1 3 x 3 + x 2 - 8 x + 5 ) M C = x 2 + 2 x - 8 Hence, marginal cost is x 2 + 2 x - 8 .

Given the total cost function for x units of a commodity as C ( x ) = 1 3 x 3 + x 2 - 8 x + 5 . Find average cost function.

Given, cost function C ( x ) = 1 3 x 3 + x 2 - 8 x + 5 Average cost function A C = Total cost Number of units A C = 1 3 x 3 + x 2 - 8 x + 5 x A C = 1 3 x 2 + x - 8 + 5 x Hence, average cost function is 1 3 x 2 + x - 8 + 5 x .

Given the total cost function for x units of a commodity as C ( x ) = 1 3 x 3 + x 2 - 8 x + 5 , find slope of average cost function.

Given, cost function C ( x ) = 1 3 x 3 + x 2 - 8 x + 5 Average cost function A C = Total cost Number of units A C = 1 3 x 3 + x 2 - 8 x + 5 x A C = 1 3 x 2 + x - 8 + 5 x Slope of average cost function = d d x ( 1 3 x 2 + x - 8 + 5 x ) = 2 3 x + 1 - 5 x 2 Hence, Slope of average cost function is 2 3 x + 1 - 5 x 2 .

E M B I B E

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 14

EASY

12th ICSE

IMPORTANT

Earn 100

If $p = \frac{100}{q + 2} - 4$ represents the demand function for a product where $p$ is the price per unit when $q$ units are sold, find the marginal revenue.

Important Questions on Application of Calculus in Commerce and Economics

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 15

A company finds that total revenue from sale of

q

units of its product is

2 q

rupees whereas the cost is

500 + \frac{1}{2} {(\frac{q}{20})}^{2}

. Find the rate of change of profit when

q = 500

.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 16

Given the total cost function for

x

units of a commodity as

C (x) = \frac{1}{3} x^{3} + x^{2} - 8 x + 5

, find the marginal cost function.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 16

Given the total cost function for

x

units of a commodity as

C (x) = \frac{1}{3} x^{3} + x^{2} - 8 x + 5

. Find average cost function.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 16

Given the total cost function for

x

units of a commodity as

C (x) = \frac{1}{3} x^{3} + x^{2} - 8 x + 5

, find slope of average cost function.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 17

If the cost function of a production unit is

C (x) = 40 - 20 x + 10 x^{2}

, find the average cost function and the output x where average cost is minimum. Verify that the average cost is equal to the marginal cost at this level of output.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 2>Chapter 1 - Application of Calculus in Commerce and Economics>EXERCISE>Q 18

The demand function of a monopolist is