NCERT Solutions for Class 12 Maths Chapter 6 Applications of Derivatives

By referring to these NCERT Maths Textbook Class 12 Chapter 6 solutions, students can learn the mathematical process of solving problems related to real-life applications, such as finding the rate of change or optimizing functions. NCERT Class 12th Maths Chapter 6 exercise solutions are curated to simplify these concepts with solved examples and detailed explanations. Whether you are solving for miscellaneous exercises or specific important questions, these mathematics solutions are a reliable resource. For students seeking assistance in Hindi or English, the Applications of Derivatives Class 12 NCERT math solutions are available in PDF format for easy download.

Step-by-Step NCERT Textbook Solutions for Class 12 Maths Chapter 6 Exercises

NCERT Textbook solutions for Class 12 Maths Chapter 6 exercises include a detailed breakdown of problems involving tangents and normals, helping students understand how to compute slopes of curves at given points. The Applications of Derivatives NCERT simple solutions PDF also focus on identifying turning points and studying their impact on the behavior of functions.

To enhance learning, students can use Class 12 Maths Textbook Chapter 6 NCERT Complete solutions by experts who provide clear and concise explanations. These solutions are designed to build a solid foundation for competitive exams by solving important questions step by step. Students preparing for board exams can benefit from these solutions as they align with the syllabus. NCERT PDF solutions for Class 12 Math Book Chapter 6 solved examples are helpful for understanding real-world applications like optimization and cost minimization.

Detailed Download of Applications of Derivatives Class 12 NCERT Book Solutions

For Board preparation, students can access Applications of Derivatives Class 12 NCERT mathematics solutions online and download. NCERT Textbook solutions for Class 12 Maths Chapter 6 PDF download offers systematic solutions to every problem, including miscellaneous exercises, with step-by-step mathematical explanations and derivations. NCERT Mathematics solutions focus on important calculus-based concepts such as derivatives, their applications in analyzing the behavior of functions and solving optimization problems. NCERT Class 12th Math solutions also include video lectures to provide a deeper mathematical insight into solving challenging problems related to increasing and decreasing functions and curve sketching.

Students can rely on the Class 12 Maths Chapter 6 NCERT solutions free download to practice and master key calculus concepts at their own pace. From detailed solved examples to critical important questions, this resource ensures learners develop confidence in applying mathematical techniques in their exams. Available in both English and Hindi, these NCERT textbook solutions use a clear and logical mathematical approach, making the study of Applications of Derivatives both engaging and practical for students.

Important Points in Class 12 Maths Chapter 6 Applications of Derivatives for Exams

Key points in Applications of Derivatives include understanding increasing and decreasing functions, solving tangents and normals, finding maxima and minima and analyzing the rate of change of quantities. Focus on Class 12 Maths Chapter 6 important questions, solved examples and miscellaneous exercises for thorough exam preparation.

Class XII Maths Chapter 6 exercise 6.3, 6.2, 6.1 (rate of change, increasing decreasing, and maxima minima) in PDF format for new academic session 2024-25. 12th NCERT solutions for math subject are modified according to CBSE exams. UP Board Intermediate students can take help from these solutions. Grade 12th Math chapter 6 solutions are given here in Hindi and English Medium with Videos explanation.

1. The sides of an equilateral triangle are increasing at the rate of 2 cm/sec. Find the rate at which its area increases, when side is 10 cm long. [CBSE Sample Paper 2017]
2. The volume of a sphere is increasing at the rate of 3 cubic centimeter per second. Find the rate of increase of its surface area, when the radius is 2 cm. [Delhi 2017]
3. The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm? [Delhi 2015]
4. Determine for what values of x, the function f(x) = x³ + 1/x³, where x ≠ 0, is strictly increasing or strictly decreasing. [CBSE Sample Paper 2017]
5. Show that the function f(x) = 4x³ – 18x² + 27x – 7 is always increasing on R. [Delhi 2017]
6. Find the interval in which f(x) = sin 3x – cos 3x, 0 < x < π, is strictly increasing or strictly decreasing. [Delhi 2016]
7. Find the point on the curve y = x³ – 11x + 5 at which the tangent is y = x – 11. [CBSE Sample Paper 2017]

1. Find the equation of tangents to the curve y = cos(x + y), where x lies in [- 2π, 2π], that are parallel to the line x + 2y = 0. [Foreign 2016]
2. Find the shortest distance between the line x – y + 1 = 0 and the curve y² = x. [CBSE Sample Paper 2017]
3. If the sum of lengths of the hypotenuse and a side of a right angled triangle is given, show that the area of the triangle is maximum, when the angle between them is π/3. [Delhi 2017]
4. Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3. Also find maximum volume in terms of volume of the sphere. [Delhi 2016]
5. The sum of the surface areas of a cuboid with sides x, 2x and x/3 and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if x is equal to three times the radius of the sphere. Also find the minimum value of the sum of their volumes. [Foreign 2016]

6. A tank with rectangular base and rectangular sides open at the top is to be constructed so that its depth is 3 m and volume is 75 cubic meter. If building of tank costs ₹ 100 per square metre for the base and ₹ 50 per square meters for the sides, find the cost of least expensive tank. [Delhi 2015C]
7. A point on the hypotenuse of a right triangle is at distances ‘a’ and ‘b’ from the sides of the triangle. Show that the minimum length of the hypotenuse is (a²/³ + b²/³)³/². [Delhi 2015C]
8. Find the local maxima and local minima, of the function f(x) = sin x – cos x, 0 < x < 2π. Also find the local maximum and local minimum values. [Delhi 2015]