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NCERT Solutions

Class 12 Maths

Application of Derivatives

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  • Ex.6.1 Q.1
  • Ex.6.1 Q.2
  • Ex.6.1 Q.3
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  • Ex.6.1 Q.18
  • Ex.6.2 Q.1
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  • Ex.6.3 Q.1
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  • Ex.6.3 Q.27
  • Ex.6.4 Q.1
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  • Ex.6.4 Q.6
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  • Ex.6.5 Q.1
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  • Ex.3.5 Q.19
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  • Ex.6.5 Q.27
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  • Ex.Misc.Q.1
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  • Ex.Misc.Q.23
  • Ex.Misc.Q.24
  • Ex.2.2 Q.21

Ex.6.2 Q.12

Which of the following functions are strictly decreasing on (0, π/2)?                                             

(A) cos x                        

(B) cos 2x                          

(C) cos 3x                         

(D)tan x

(A) Let f(x) = cos x

So, f’(x) = -sin x

In interval (0, π/2), f’(x) = -sin x < 0

So, f(x) = cos x is strictly decreasing in interval (0, π/2)

(B) Let f(x) = cos 2x

So, f’(x) = -2 sin 2x

Now, 0 < x < π/2

⟹  0 < 2x < π

⟹  sin 2x > 0

⟹ -2 sin 2x < 0

So, f(x) = cos 2x is strictly decreasing in interval (0, π/2).

(C) Let f(x) = cos 3x

So, f’(x) = -3 sin 3x

Now, f’(x) = 0

 -3 sin 3x = 0

  sin 3x = 0

  3x = π as x є (0, π/2)

  x =  

The point x = π3 divides the interval (0, ) into two disjoint intervals i.e. (0,  ) and  ( ,  ).

Now, in interval (0, π/3), f’(x) = -3 sin 3x < 0              [As 0 < x <  ⟹ 0 < 3x < π]

So, f(x) = cos 3x is strictly decreasing in interval (0, )

However in interval ( , ), f’(x) = -3 sin 3x > 0  [As  < x <   π < 3x < ]

So, f(x) = cos 3x is strictly increasing in interval ( , )

So, f(x) = cos 3x is neither increasing nor decreasing in the interval (0, π/2).

(A) Let f(x) = tan x

So, f’(x) = sec2 x

In interval (0, ), f’(x) = sec2 x > 0

So, f(x) = tan x is strictly increasing in interval (0, ).

Therefore, functions cos x and cos 2x are strictly decreasing in (0, ).

Hence, the correct answers are A and B.

Video solution:

Application of Derivatives Class 12 Maths NCERT Chapter 6 NCERT Solutions

Solving NCERT textbook questions of Application of Derivatives Class 12 Maths NCERT Chapter 6 is a crucial step to gauge your understanding of the concepts. It provides you with an opportunity to assess your grasp of the material after learning each chapter. We have already provided solutions to all the exercises in the NCERT textbook of Class 12 Maths Application of Derivatives, available in various formats such as video, text, and downloadable PDFs. If you need assistance with any of the NCERT questions or any other academic topics, feel free to ask in the “Ask Questions” section of LearnoHub.com.

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In conclusion, studying each line and solving all the questions of NCERT textbooks is an essential part of the learning process. It ensures a strong foundation, deep understanding, and overall academic growth.

How to make the most of NCERT Solutions module of Application of Derivatives Class 12 Maths NCERT Chapter 6 on LearnoHub.com?

Using the NCERT solutions module effectively can significantly enhance your learning experience and understanding of the subject matter. Here's a step-by-step guide on how to make the most out of the NCERT solutions:

  1. Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
  2. Match with Our Solution: After attempting the question, compare your result and approach with the provided NCERT solution. This step allows you to identify any mistakes or gaps in your understanding.
  3. Refer to Solution Video (if needed): If you encounter difficulty or are unable to solve a question, you can refer to the NCERT solution video on Application of Derivatives Class 12 Maths NCERT Chapter 6 to get a step-by-step explanation of the correct approach. Pay attention to the reasoning and methodology used in the video.
  4. Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
  5. Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
  6. Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 12 Maths Application of Derivatives Online Test on LearnoHub.com.
  7. Review and Revise: Regularly review the concepts and solutions you've learned. Revise your notes and practice regularly to retain the knowledge effectively. You may refer Application of Derivatives Class 12 Maths Notes.
  8. Ask for Clarification: If you encounter any doubts or have questions about the solutions, don't hesitate to seek clarification on the “Ask Questions” section of LearnoHub.com. Application of Derivatives Class 12 Maths NCERT Chapter 6 Questions.

By following these steps and actively engaging with the NCERT solutions module of Class 12 Maths Application of Derivatives NCERT Chapter 6, you can improve your learning outcomes, develop a better grasp of the subject, and perform well in exams and other academic assessments. Remember that consistent practice, understanding, and application of knowledge are key to academic success.

NCERT solutions of Application of Derivatives Class 12 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 12 Maths Application of Derivatives NCERT solutions.

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