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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.15
  • Ex.6.1 Q.16
  • Ex.6.1 Q.17
  • Ex.6.1 Q.18
  • Ex.6.2 Q.1
  • Ex.6.1 Q.2
  • Ex.6.2 Q.3
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  • Ex.6.2 Q.5
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  • Ex.6.2 Q.10
  • Ex.6.2 Q.11
  • Ex.6.2 Q.12
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  • Ex.6.2 Q.15
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  • Ex.6.2 Q.18
  • Ex.6.2 Q.19
  • Ex.6.3 Q.1
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  • Ex.6.3 Q.14
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  • Ex.6.3 Q.24
  • Ex.6.3 Q.25
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  • Ex.6.3 Q.27
  • Ex.6.4 Q.1
  • Ex.6.4 Q.2
  • Ex.6.4 Q.3
  • Ex.6.4 Q.4
  • Ex.6.4 Q.5
  • Ex.6.4 Q.6
  • Ex.6.4 Q.7
  • Ex.6.4 Q.8
  • Ex.6.4 Q.9
  • Ex.6.5 Q.1
  • Ex.6.5 Q.2
  • Ex.6.5 Q.3
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  • Ex.6.5 Q.5
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  • Ex.3.5 Q.19
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  • Ex.6.5 Q.21
  • Ex.6.5 Q.22
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  • Ex.6.5 Q.25
  • Ex.6.5 Q.26
  • Ex.6.5 Q.27
  • Ex.6.5 Q.28
  • Ex.6.5 Q.29
  • Ex.Misc.Q.1
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  • Ex.Misc.Q.5
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  • Ex.Misc.Q.15
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  • Ex.Misc.Q.20
  • Ex.Misc.Q.21
  • Ex.Misc.Q.22
  • Ex.Misc.Q.23
  • Ex.Misc.Q.24
  • Ex.2.2 Q.21

Ex.6.5 Q.15

Find two positive numbers x and y such that their sum is 35 and the product x2y5 is a maximum.

Let one number be x. Then, the other number is y = (35 − x).

Let f(x) = x2y5

⟹  f(x) =  x2(35 - x)5

So, f’(x) = 2x (35 - x)5 - 5x2(35 - x)4

⟹  f’(x) = x(35 - x)4[2(35 - x) – 5x]

⟹  f’(x) = x(35 - x)4[70 - 2x – 5x]

⟹  f’(x) = x(35 - x)4(70 - 7x)

Now, f’(x) = 0

⟹  x(35 - x)4(70 - 7x) = 0

⟹  x = 0, 35, 10

Again f”(x) = 7(35 - x)4(10 - x) + 7x[-(35 - x)4 – 4(35 - x)3(10 - x)]

⟹  f”(x) = 7(35 - x)4(10 - x) - 7x (35 - x)4 – 28x(35 - x)3(10 - x)

⟹  f”(x) = 7(35 - x)3[(35 - x)(10 - x) - x(35 - x) – 4x (10 - x)]

⟹  f”(x) = 7(35 - x)3[350 – 45x + x2 – 35x + x2 – 40x + 4x2]

⟹  f”(x) = 7(35 - x)3(6x2 – 120x + 350)

When x = 35, y = 35 – 35 = 0 and the product x2y5 will be equal to 0.

When x = 0, y = 35 − 0 = 35 and the product x2y5 will be 0.

So, x = 0 and x = 35 cannot be the possible values of x.

When x = 10, we have

f”(x) = 7(35 - 10)3(6 (10)2 – 120 (10) + 350)

         = 7(25)3(-250)

         < 0  

So, By second derivative test, P(x) will be the maximum when x = 10 and

 y = 35 − 10 = 25

Hence, the required numbers are 10 and 25.

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.

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  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.
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  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.
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  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.
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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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