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NCERT Solutions for Class 12 Maths Chapter 6 Exercise 6.2 Application of Derivatives - PDF Download

JEE Mains & Advanced

NCERT solutions for class 12 maths chapter 6 exercise 6.2 Application of Derivatives focuses on applying differentiation to figure out if a function is increasing or decreasing for a particular range. Students can easily utilize these properties of derivatives by understanding them. This topic is very relevant to real life, thus it requires a lot of practice and revision. Class 12 maths chapter 6 exercise 6.2 NCERT solutions are prepared by the academic team of mathematics at eSaral. These solutions provide a deep understanding of the concept of increasing and decreasing functions to prepare for exams.

Ex 6.2 class 12 maths chapter 6 consists of 19 questions that teach students how to apply derivatives to increasing and decreasing functions. Students can easily solve all the questions of ex 6.2 class 12 maths by practicing NCERT solutions. These solutions are also available in a free PDF that will help you to practice all the questions and score good marks in exams . You can download the PDF from the link given below.

Topics Covered in Exercise 6.2 Class 12 Mathematics Questions

Ex 6.2 class 12 maths ch 6 covers the concept of increasing and decreasing functions. You can check a detailed explanation of this topic provided below.

1.

Increasing and Decreasing Functions

  1. Increasing and Decreasing Functions - If the first derivative in a range is positive, the function is increasing in that range; conversely, if the derivative is negative, the function is decreasing in that range. For example, When a given function, y = F(x), has a value that increases as x increases, it is said to be an increasing function; conversely, if y's value decreases as x increases, it is said to be a declining function.

Let I be an interval contained in the domain of a real valued function f. Then f is said to be

(i) increasing on I if x1 < x2 in I ⇒ f(x1 ) < f(x2 ) for all x1 , x2 ∈ I.

(ii) decreasing on I, if x1 , x2 in I ⇒ f(x1 ) < f(x2 ) for all x1 , x2 ∈ I.

(iii) constant on I, if f(x) = c for all x ∈ I, where c is a constant.

(iv) decreasing on I if x1 < x2 in I ⇒ f (x1 ) ≥ f(x2 ) for all x1 , x2 ∈ I

(v) strictly decreasing on I if x1 < x2 in I ⇒ f(x1 ) > f(x2 ) for all x1 , 2 ∈ I

Let x0 be a point in the domain of definition of a real valued function f. Then f is said to be increasing, decreasing at x0 if there exists an open interval I containing x0 such that f is increasing, decreasing, respectively, in I.

Theorem 1: Let f be continuous on [a, b] and differentiable on the open interval (a,b). Then

(a) f is increasing in [a,b] if f ′(x) > 0 for each x ∈ (a, b)

(b) f is decreasing in [a,b] if f ′(x) < 0 for each x ∈ (a, b) 

(c) f is a constant function in [a,b] if f ′(x) = 0 for each x ∈ (a, b)

Tips for Solving Exercise 6.2 Class 12 Chapter 6 Application of Derivatives

Ex 6.2 can be solved by following the tips provided by subject experts of eSaral.

  1. The NCERT solutions for class 12 maths chapter 6 ex 6.2 is a fantastic resource designed to help students precisely master formulas and properties related to different kinds of increasing and decreasing functions. Students must study these solutions to achieve good marks in exams.

  2. Before solving exercise 6.2, you have to learn all the related formulas and theorems of increasing and decreasing functions.

  3. You should also solve examples related to the concept of increasing and decreasing functions to gain a clear understanding of questions.

Importance of Solving Ex 6.2 Class 12 Maths Chapter 6 Application of Derivatives

You will get a lot of benefits by solving ex 6.2 class 12 maths chapter 6. Some of them are mentioned below.

  1. NCERT solutions class 12 maths chapter 6 exercise 6.2 includes formulas and theorems which provides a step-by-step understanding of the whole exercise in an organized manner. 

  2. By understanding the pattern of questions provided in these solutions students can easily prepare for board exams and various competitive tests. 

  3. NCERT solutions of ex 6.2 class 12 maths also have included important examples and questions which provides you a clear understanding of methods to solve questions in exams.

  4. NCERT solutions for ex 6.2 class 12 maths ch 6 not only helps you to complete your school assignments but also helps you to build a strong foundation to solve questions in competitive exams. 

Frequently Asked Questions

If the value of y increases as the value of x increases for a function y = f(x), then the function is called an increasing function.

If the value of y decreases on increasing the value of x for a function y = f(x), the function is said to be decreasing.

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