# NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

## NCERT Solutions for Class 12 Maths Chapter 6 â€“ Free PDF Download

The NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives provides answers for all the questions listed under this chapter which is included in the Class 12 Maths CBSE Syllabus for 2023-24. These NCERT Solutions include a complete set of questions and answers organised with an advanced level of difficulty, which provides students with sufficient opportunity to apply their skills. Students can download these NCERT Solutions for Class 12 MathsÂ and strengthen their skills.

## Access Answers to NCERT Class 12 Maths Chapter 6 Application of Derivatives

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### NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

This chapter of NCERT Solutions for Class 12 Maths mainly has a set of topics like The rate of change of quantities, Increasing and decreasing functions, Tangents and normals, Approximations, Maxima and minima and many more. Some of the important concepts are:

1. A function f is said to be

(a) increasing on an interval (a, b) if x1 < x2 in (a, b) â‡’ f(x1) < f(x2) for all x1, x2 âˆˆ (a, b)

(b) decreasing on (a,b) if x1 < x 2 in (a, b) â‡’ f(x1 ) > f(x2 ) for all x1 , x2 âˆˆ (a, b)

(c) constant in (a, b), if f (x) = c for all x âˆˆ (a, b), where c is a constant

2. First Derivative Test

3. Second Derivative Test

Students can utilise the NCERT Solutions for Class 12 Maths Chapter 6 for quick references to comprehend key and complex topics.

### NCERT Solutions for Class 12 Maths Chapter 6 Exercises

Get detailed NCERT Solutions for all the questions listed under the below exercises:

Exercise 6.1 Solutions: 18 Questions (10 Long, 6 Short, 2 MCQs)

Exercise 6.2 Solutions: 19 Questions (10 Long, 7 Short, 2 MCQs)

Exercise 6.3 Solutions: 27 Questions (14 Long, 11 Short, 2 MCQs)

Exercise 6.4 Solutions: 9 Questions (7 Short, 2 MCQs)

Exercise 6.5 Solutions: 29 Questions (15 Long, 11 Short, 3 MCQs)

Miscellaneous Exercise Solutions: 24 Questions (14 Long, 4 Short, 6 MCQs)

### NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

The main topics covered inÂ NCERT Solutions for Class 12 Chapter 6 Application of Derivatives are:

 Exercise Topic 6.1 Introduction 6.2 Rate of Change of Quantities 6.3 Increasing and Decreasing Functions 6.4 Tangents and Normals 6.5 Approximations 6.6 Maxima and Minima Others Miscellaneous Q&A

### Key Features of NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives

1. NCERT Solutions will help in boosting studentsâ€™ confidence levels.
2. The content is well-structured so that it becomes easier for students to learn and understand.
3. NCERT Solutions are based on the latest CBSE syllabus for 2023-24.
4. This chapter will help the students to strengthen their foundation on the application of derivatives.
5. NCERT Solutions are a valuable aid for students in their assignments and competitive exams.

Disclaimer â€“Â

Dropped Topics â€“Â 6.4 Tangents and Normals, 6.5 Approximations, Examples 45, 46, Ques. 1, 4â€“5 and 20â€“24 (Miscellaneous Exercise), Page 245 Points 4â€“10 in the Summary

## Frequently Asked Questions on NCERT Solutions for Class 12 Maths Chapter 6

Q1

### Give me an overview of Chapter 6 of NCERT Solutions for Class 12 Maths.

This chapter has an overall of six topics/subtopics with miscellaneous questions and answers at the end. Provided below is the list of topics discussed in this chapter.
6.1 â€“ Introduction
6.2 â€“ Rate of Change of Quantities
6.3 â€“ Increasing and Decreasing Functions
6.4 â€“ Tangents and Normals
6.5 â€“ Approximations
6.6 â€“ Maxima and Minima
Q2

### Why should I download BYJUâ€™S NCERT Solutions for Class 12 Maths Chapter 6?

There are numerous reasons why you should download the NCERT Solutions for Class 12 Maths Chapter 6, designed by the experts at BYJUâ€™S.
1. The CBSE board recommends the students refer to the NCERT textbooks as it is one of the best study materials from the exam point of view.
2. NCERT Solutions plays a significant role as the answers to all the questions present in the NCERT textbook are available in one place.
3. The subject matter experts and faculty at BYJUâ€™S provide solutions in a concise manner to help students score well in the board exams.
Q3

### What are the main applications of derivatives in our daily life according to NCERT Solutions for Class 12 Maths Chapter 6?

Derivatives are used to determine the rate of change, intervals of increasing or decreasing, Lagrangeâ€™s Mean Value Theorem, Rolleâ€™s Theorem, a point when tangent is parallel or perpendicular, the slope of tangent or normal, an approximate value of numbers etc. These applications are explained in simple and understandable language by our team of experts in order to help students to obtain a clear idea about the important concepts. Numerous examples are provided under each application to improve conceptual knowledge among students irrespective of their intelligence quotient.