NCERT Solutions for Class 12 Help.html Mathematics Part I Chapter 6 Application Of Derivatives

Application Of Derivatives Here is the CBSE Help.html Chapter 6 for Class 12 students. Summary and detailed explanation of the lesson, including the definitions of difficult words. All of the exercises and questions and answers from the lesson's back end have been completed. NCERT Solutions for Class 12 Help.html Application Of Derivatives Chapter 6 NCERT Solutions for Class 12 Help.html Application Of Derivatives Chapter 6 The following is a summary in Hindi and English for the academic year 2025-26. You can save these solutions to your computer or use the Class 12 Help.html.

Question 1

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Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm.

Solution

Let A be area of circle of radius r

therefore space space space space space space space space space space space straight A space equals space πr squared

Rate of change of area with respect to

straight r space equals space dA over dr

equals space straight d over dr left parenthesis πr squared right parenthesis space equals space 2 πr

when r = 5, rate of change of area =

2 straight pi space cross times space 5 space equals space 10 straight pi space cm squared divided by cm

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NCERT Solutions for Class 12 Help.html Mathematics Part I Chapter 6 Application Of Derivatives

Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm.

Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm (b) r = 4 cm

Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2 m?

How fast is the volume of a ball changing with respect to its radius when the radius is 3 m?

A balloon which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the latter is 10 cm.

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x³- 0.02 x²+ 30 x + 5000.
Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007 x – 0.003 x² + 15 x + 4000.
Find the marginal cost when 17 units are produced.

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x² +36x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant.

The total revenue in Rupees received from the sale of x units of a product is given by
R(x) = 13x² + 26x + 15.
Find the marginal revenue when x = 7.

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NCERT Solutions for Class 12 Help.html Mathematics Part I Chapter 6 Application Of Derivatives

Find the rate of change of the area of a circle with respect to its radius r when r = 5 cm.

Find the rate of change of the area of a circle with respect to its radius r when(a) r = 3 cm (b) r = 4 cm

Find the rate of change of the volume of a ball with respect to its radius r. How fast is the volume changing with respect to the radius when the radius is 2 m?

How fast is the volume of a ball changing with respect to its radius when the radius is 3 m?

A balloon which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the latter is 10 cm.

The cost function C(x), in rupees, of producing x items (x ≥ 15) in a certain factory is given by Determine the marginal cost function and the marginal cost of producing 100 items.

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x3 - 0.02 x2 + 30 x + 5000.Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007 x – 0.003 x2 + 15 x + 4000.Find the marginal cost when 17 units are produced.

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x2 +36x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant.

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 13x2 + 26x + 15.Find the marginal revenue when x = 7.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Find the rate of change of the area of a circle with respect to its radius r when
(a) r = 3 cm (b) r = 4 cm

The total cost C(x) in Rupees, associated with the production of x units of an item is given by C(x) = 0.005 x³- 0.02 x²+ 30 x + 5000.
Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

The total cost C(x) in Rupees associated with the production of x units of an item is given by C(x) = 0.007 x – 0.003 x² + 15 x + 4000.
Find the marginal cost when 17 units are produced.

The total revenue in Rupees received from the sale of x units of a product is given by R(x) = 3x² +36x + 5. Find the marginal revenue, when x = 5, where by marginal revenue we mean the rate of change of total revenue with respect to the number of items sold at an instant.

The total revenue in Rupees received from the sale of x units of a product is given by
R(x) = 13x² + 26x + 15.
Find the marginal revenue when x = 7.