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NCERT Solutions for Class 12 Maths Chapter 6 – Application of Derivatives Exercise 6.2

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Chapter 6 – Application of Derivatives Exercise 6.2

1.

NCERT Class 12 problem on increasing and decreasing functions – Q1

Solution showing function increasing-decreasing using derivative – Q1 Answer

2.

Determine function behavior using derivatives – Exercise 6.2 Q2

Derivative-based behavior analysis of function – Q2 Answer Image

3.

Application of derivative to test monotonicity – Q3 Maths Class 12

Solved increasing/decreasing test via first derivative – Q3

4.

NCERT question on derivative sign and function growth – Q4

Monotonicity explained using derivative sign – Q4 Answer

5.

Problem on critical points and increasing intervals – Q5 Chapter 6

NCERT Answer: Determine intervals using critical
points – Q5

6.

Advanced test for monotonicity using first derivative – Q6 NCERT

Start of detailed solution on monotonicity test – Q6 step 1

Interval testing and derivative steps – Q6 step-2

Conclusion for Q6 increasing/decreasing analysis – step-5

7.

Behavior of function via first derivative test – Q7 Class 12 Maths

Initial analysis of function’s derivative – Q7 Part 1

Sign chart and derivation steps – Q7 step-2

8.

Check increasing-decreasing nature of function – Q8 NCERT

Solved example of function nature from derivative – Q8 Answer-step-2

9.

Apply derivative to analyze curve intervals – Q9 Exercise 6.2

Breakdown of function derivative for monotonicity – Q9 step-1

Detailed sign analysis for Q9 function – step-2

10.

Class-12 Applications of Derivatives Exercise 6.2 Question 10-Evaluate function's monotonicity from derivative - NCERT

Class-12 application of Derivatives Exercise 6.2 Question 10 First derivative sign chart applied to solve- NCERT Answer

11.

Class-12 Applications of Derivatives Exercise 6.2 Question 11-Class 12 question on interval-based function behavior - NCERT

Class-12 application of Derivatives Exercise 6.2 Question 11 Step-by-step solution for monotonicity - NCERT Answer

12.

Class-12 Applications of Derivatives Exercise 6.2 Question 12-Detailed problem on curve analysis using derivatives- NCERT

Class-12 application of Derivatives Exercise 6.2 Question 12 Interval checking and sign table- (a),(b) NCERT Answer-(a),(b)

Class-12 application of Derivatives Exercise 6.2 Question 12 Function behavior breakdown with derivative- (c) NCERT Answer-(c)

13.

Class-12 Applications of Derivatives Exercise 6.2 Question 13-Find intervals of increase/decrease with derivative - NCERT

Class-12 application of Derivatives Exercise 6.2 Question 13 “Derivative sign used to solve function nature – NCERT Answer

14.

Class-12 Applications of Derivatives Exercise 6.2 Question 14-First derivative used to determine function nature- NCERT

Class-12 application of Derivatives Exercise 6.2 Question 14 Interval-based behavior of function- NCERT Answer

15.

Class-12 Applications of Derivatives Exercise 6.2 Question 15-Analyze behavior of rational functions using calculus - NCERT

Class-12 application of Derivatives Exercise 6.2 Question 15 Analyzing rational function with first derivative- NCERT Answer

Class-12 application of Derivatives Exercise 6.2 Question 15 Derivative charting and testing of intervals- NCERT Answer

16.

Class-12 Applications of Derivatives Exercise 6.2 Question 16-Function analysis using sign of derivative- NCERT

Class-12 application of Derivatives Exercise 6.2 Question 16 Use of calculus in behavior test – Q16 NCERT Answer- NCERT Answer

17.

Class-12 Applications of Derivatives Exercise 6.2 Question 17-Check monotonic nature of trigonometric function- NCERT

Class-12 application of Derivatives Exercise 6.2 Question 17 Solved derivative test on trigonometric function - NCERT Answer

18.

Class-12 Applications of Derivatives Exercise 6.2 Question 18-Apply derivative test on algebraic function- NCERT

Class-12 application of Derivatives Exercise 6.2 Question 18 Solved algebraic function derivative analysis- NCERT Answer

19.

Class-12 Applications of Derivatives Exercise 6.2 Question 19-“Behavior testing of polynomial function using derivative - NCERT

Class-12 application of Derivatives Exercise 6.2 Question 19 Solution - NCERT Answer

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Class 12 Maths Chapter 6 – Application Of Derivatives: All Exercises

Exercise	Link
Exercise 6.1	View Solutions
Exercise 6.3	View Solutions
Miscellaneous Exercise	View Solutions

Class 12 Application Of Derivatives- Exercise 6.2 Overview

Exercise 6.2 centres on a strong idea in calculus—increasing and decreasing functions. Using the first derivative, it enables students to spot where a function is either expanding, declining, or constant. Whether you’re examining the rise and fall of profit, demographic patterns, or any other dynamic system, calculus begins to feel like a potent tool for real-world interpretation.

Application of Derivatives Class 12 NCERT Solutions Exercise 6.2 guides students through issues where they apply derivative sign analysis to ascertain the kind of functions. It’s about learning to interpret behaviour rather than only about fixing problems. Later on, this makes the practice valuable for science, economics, and even machine learning foundations.

Complementing the 2025 NCERT syllabus, this activity expands the fundamental idea of the derivative to logical and visual comprehension. The given answers help students understand deeper insights into function behaviour by breaking out how to step-by-step study a function and identify where it increases or declines.

Working through the Application of Derivatives Class 12 NCERT Solutions Exercise 6.2 helps students improve their mathematics tools and develop critical thinking ability. Those getting ready for tests like JEE, CUET, and others where interpretation is crucial would greatly benefit from this activity.

FAQs – Application Of Derivatives Class 12 Exercise 6.2 NCERT

Why is knowing increasing/decreasing functions significant?

In business (profit/loss), science (growth/decay), and technology (data patterns), this idea finds application.

Where might a function rise or fall from?

Examining the sign of the first derivative reveals that the function is increasing if f′(x) > 0; it is decreasing if f′(x) < 0.

I consistently find the sign for f′(x) incorrect. What action ought I to take?

Key for accuracy is to double-check your derivative and properly enter plug values in the interval.

How do I choose test points to locate intervals?

Solving f′(x) = 0 will help you to choose values inside the intervals you design. These test sites let you check the sign.

Could I graph the function using a calculator?

While studying, calculators or graphing tools can aid; for board tests, you should rely on hand graphs and analysis.