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Easy Concept Development with RD Sharma Class 12 Maths Solutions Chapter 15 - Mean Value Theorems

Last updated date: 27th May 2024
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RD Sharma Solutions for Class 12 Maths Chapter 15 - Mean Value Theorems - Free PDF Download

Calculus is supported by an essential theory called the Mean Value Theorem. It is needed to get accuracy in calculus. A clear understanding of the concept of the Mean Value Theorem is necessary to do well in Calculus. Hence, solving RD Sharma is required to achieve both clarity of concepts and confidence in this topic. The solution file for this chapter will enable you to grab the concepts well and to complete preparing them exceptionally.

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Significance of RD Sharma Class 12 Chapter 15 Solutions

Mean Value Theorem is one of the most important topics in Continuity and Differentiability. The RD Sharma class 12 Mean Value Theorem Solutions are prepared by the best experts on the subject to give an excellent learning experience for the students. All the solutions of RD Sharma Class 12 Maths Chapter 15 Solutions are according to the CBSE guidelines so these solutions are also helpful for students to prepare for their board exams. In order to master the Mean Value Theorem concepts, students can download the free PDF solution available on Vedantu.

About Mean Value Theorem

The Mean Value Theorem enables one to infer that the converse is also valid. If f'(x)=0 for all x in some interval, then f(x) is constant over that interval. This outcome will seem intuitively evident, but it has major consequences that are not obvious. Let us discuss the important concepts of the Mean Value Theorem chapter.

  • Rolle’s theorem 

  • Geometrical interpretation of Rolle’s theorem

  • Algebraic interpretation of Rolle’s theorem

  • Applicability of Rolle’s theorem

  • Verification of Rolle’s theorem by using a function that is defined on a given interval

  • Miscellaneous applications of Rolle’s theorem

We have provided step-by-step solutions for all exercise questions given in the pdf of Class 12 RD Sharma Chapter 15 - Mean Value Theorems. All the Exercise questions with solutions in Chapter 15 - Mean Value Theorems are given below:

Download this solution file for Class 12 RD Sharma Chapter 15 for your convenience. Learn how the experts of Vedantu have perfectly solved the problems using the concepts. Understand how you can correctly solve the problems without wasting time and can score well in the board exams. 

FAQs on Easy Concept Development with RD Sharma Class 12 Maths Solutions Chapter 15 - Mean Value Theorems

1. What is the Mean value theorem?

The Mean Value Theorem states that if a function f(x) is continuous and differentiable in the interval between a and b with b>a then there will be some point c in between a and b for which f’(c) is actually the slope of the line joining the coordinates (a, f(a)) and (b, f(b)). The Mean Value Theorem is a theory in calculus that has the ability to prove various results relating to the local value and the global property of a particular.

2. What is the importance of the Mean value Theorem?

Mean Value Theorem proves the existence of a point in between two continuous differentiable points. The most common application of the Mean Value Theorem is Rolle’s theorem which is a special case of the Mean Value Theorem. Problems of Rolle’s theorem and other such kinds of problems need a guarantee about the existence of a point in between two points without not even getting to know the actual value of the point. This theorem is very useful not only to prove the fundamental theorem of calculus but also in various engineering conditions while studying something of arbitrary size with a limit of the size approaching zero.

3. Why do I have to study RD Sharma Solutions of Class 12 Maths Chapter 15?

Mean Value Theorem is an important chapter and like most of the calculus chapters this chapter is also highly scoring and conceptual. This chapter bears extra weightage because this chapter is actually the theory of calculus which develops the concept of calculus among the students. However, mere developing concepts in this chapter are not enough for the students to score high. Students need continuous practice of this topic to ace their exams. 

RD Sharma is a book to practice your concepts well in an easy way.  The subject experts of Vedantu have well prepared the solutions of RD Sharma Maths Chapter 15 with detailed steps so that students can easily learn and understand the concept beyond every single step making a deep-rooted concept in them. Students can easily download the free PDF version of the solutions of RD Sharma Maths Chapter 15 from the Vedantu site to prepare themselves well for this topic.

4. What are important points to remember in the Mean Value Theorem?

Mean Value Theorem is a scoring topic and not much time is needed to score on this topic. So the right approach is to remember the most important key points on which your study about this chapter should be based. The important points to be remembered in the Mean value Theorem are as follows:

  • What is Mean Value Theorem

  • Example of Mean Value Theorem- Square root, polynomial

  • Mean Value Theorem Practice problems

  • Mean Value Theorem justification with equations

  • Establishing differentiability for Mean Value Theorem

  • Mean Value Theorem Application both in real life

  • Mean Value Theorem applications in calculus and engineering

  • Review and revision of Mean Value Theorem

5. How important is it to cover Mean Value Theorem to Class?

Mean Value Theorem is the theoretical background of calculus. A student needs to learn and understand the theory first to solve problems of calculus. Mean Value Theorem can be used in many types of problems in real life and even in core science subjects like Engineering, Biology, and Chemistry. Hence it is extremely necessary for the students to have a clear concept about the theory and its applications which can make their study in other fields also easy. Engineering aspirants will miss a great needed knowledge for their advanced study without this topic. In fact, subject experts often recommend starting the study of calculus from the Mean Value Theorem itself. Hence it is rightly included in the Class 12 Maths curriculum.