NCERT Solutions Class 12 Maths Chapter 6 Application of Derivatives
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives explains the fundamental concepts and Application of Derivatives in different disciplines. The Application of Derivatives is widely found in the field of engineering, science, economics, social science, etc. When it comes to studying the various aspects of physics or engineering even the slightest miscalculation can result in huge errors. Thus, it is highly important for kids to form a firm base to apply the knowledge of derivatives and related concepts in real life. In this chapter, we will learn how the derivative can be used to determine the rate of change of quantities. It also talks about how derivatives are applied to find extreme values of functions, to determine and analyze the shapes of graphs, and to solve equations numerically.
One of the most important Application of Derivatives is to find the optimal solution to problems. For example, to find the equations of tangent and normal to a curve at a point or to find turning points on the graph of a function which in turn will help us to locate points at which the largest or smallest value (locally) of a function occurs. Derivatives are also useful in calculating the intervals on which a function is increasing or decreasing. Lastly, it is also helpful to find the approximate value of specific quantities. NCERT Solutions Class 12 Maths Chapter 6 enhances the fundamental understanding of students about the Application of Derivatives. With the regular practice of Class 12 Maths NCERT Solutions Chapter 6, students will quickly gain a deep understanding of this topic. To learn and practice with NCERT Solutions Chapter 6 Application of Derivatives, download the exercises provided in the links below.
- NCERT Solutions Class 12 Maths Chapter 6 Ex 6.1
- NCERT Solutions Class 12 Maths Chapter 6 Ex 6.2
- NCERT Solutions Class 12 Maths Chapter 6 Ex 6.3
- NCERT Solutions Class 12 Maths Chapter 6 Ex 6.4
- NCERT Solutions Class 12 Maths Chapter 6 Ex 6.5
- NCERT Solutions Class 12 Maths Chapter 6 Miscellaneous Exercise
NCERT Solutions for Class 12 Maths Chapter 6 PDF
Chapter 5 familiarizes students with the concepts of derivatives of composite, implicit, logarithmic, inverse, trigonometric and exponential functions. This lesson proceeds with learning how these derivatives are applied in different disciplines. This topic is quite useful in performing real analysis and graphical interpretation of functions. NCERT Solutions for Class 12 Maths Chapter 6 are well-crafted guides proficient in implementing a clear knowledge of the Application of Derivatives along with their properties. To practice with these solutions, click on the links of the pdf files given below.
☛ Download Class 12 Maths NCERT Solutions Chapter 6 Application of Derivatives
NCERT Class 12 Maths Chapter 6
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives
The derivatives are applied to calculate the rate of change, intervals of increasing or decreasing functions, the point when tangent is parallel or perpendicular, the approximate value of numbers, etc. All these Application of Derivatives are elaborated in an easy-to-understand and simple language by our math experts. Students can easily learn all the important concepts with the NCERT solutions Class 12 Maths Chapter 6 Application of Derivatives. To practice the exercise-wise NCERT Solutions Class 12 Maths Application of Derivatives, try the links given below.
- Class 12 Maths Chapter 6 Ex 6.1 - 18 Questions
- Class 12 Maths Chapter 6 Ex 6.2 - 19 Questions
- Class 12 Maths Chapter 6 Ex 6.3 - 27 Questions
- Class 12 Maths Chapter 6 Ex 6.4 - 9 Questions
- Class 12 Maths Chapter 6 Ex 6.5 - 29 Questions
- Class 12 Maths Chapter 6 Miscellaneous Ex - 24 Questions
Topics Covered: NCERT Solutions Class 12 Maths Chapter 6 mainly focuses on the rate of change of quantity, increasing/decreasing functions, tangents, normals, approximations, maxima, and minima. Details of the above-mentioned topics are provided through various interactive illustrations for students to grasp them better.
Total Questions: Class 12 Maths Chapter 6 Application of Derivatives has 102 questions in 6 exercises along with 24 more provided in a miscellaneous exercise. Out of these 126 questions, there are 63 long answers, 46 are short answers and the rest of the 41 are multiple-choice questions based on various topics covered under this chapter. These questions sufficiently provide the practice of all important topics from an exam point of view.
List of Formulas in NCERT Solutions Class 12 Maths Chapter 6
The Application of Derivatives is considered as one of the basic topics in learning calculus that is especially useful in optimizing the solutions of various problems. Understanding these applications requires knowledge of the rules and concepts applied in derivatives. Most of the questions require kids to employ their mathematical acumen to understand what needs to be done. As the techniques and formulas used to solve textbook sums are also utilized for combating real-life issues students must be well-versed in them. Thus NCERT Solutions Class 12 Maths Chapter 6 elaborates each of these concepts using examples some of which are given below:
- If a quantity y varies with another quantity x, satisfying some rule y = f(x), then dy/dx (or f′(x) ) represents the rate of change of y with respect to x and dy/dx x = x0 ( or f′( x 0) ) represents the rate of change of y with respect to x at x = x 0.
- A function f is said to be increasing on an interval
- (a, b) if x1 < x2 in (a, b) ⇒ f(x1) < f(x2) for all x1, x2 ∈ (a, b)
- Decreasing on (a,b) if x1 < x2 in (a, b) ⇒ f( x1) > f (x2) for all x1 , x2 ∈ (a, b)
- Constant in (a, b), if f (x) = c for all x ∈ (a, b), where c is a constant.
- In calculus, a derivative test uses the derivatives of a function to locate the critical points of a function and determine whether each point is a local maximum, a local minimum, or a saddle point. Derivative tests can also give information about the concavity of a function.
- a) First Derivative Test: The first derivative test is applied to analyze the functions using their first derivatives in order to find their extremum point.
- b) Second Derivative Test: The Second Order Derivative is the derivative of the first derivative of the given function.
FAQs on NCERT Solutions for Class 12 Maths Chapter 6
Why are NCERT Solutions Class 12 Maths Chapter 6 Important?
NCERT Solutions Class 12 Maths Chapter 6 is highly efficient to deliver deep conceptual knowledge of basics related to Application of Derivatives. There are many important concepts explained in these solutions that enable students to understand the real-life Application of Derivatives. By planning a strategic exam preparation with the help of these resources students can attain a thorough knowledge of all topics to excel in exams. The pattern of these solutions is promising in raising the mathematical quotient of students.
Do I Need to Practice all Questions Provided in NCERT Solutions Class 12 Maths Application of Derivatives?
All questions provided in NCERT Solutions Class 12 Maths Application of Derivatives are devised in a proficient manner to cover the various topics and concepts of this chapter. By solving each sum provided in the six exercises of this chapter, kids can learn the whole chapter at a steady pace. Following this simple approach will aid students to comfortably grasp the key aspects of the Application of Derivatives. This type of learning is also beneficial in preparing for various competitive exams and higher-level studies.
What are the Important Topics Covered in NCERT Solutions Class 12 Maths Chapter 6?
Chapter 6 Application of Derivatives of class 12 Maths briefly defines all the important Application of Derivatives in a simple and understandable language. Some of the important concepts explained in NCERT Solutions Class 12 Maths Chapter 6 chapter are based on applying derivatives to find out the rate of change of quantities, determining intervals, solving the equation of the tangent and the normal line to a curve at a given point. The main objective of these solutions is to encourage practice and math learning in students to help them in their studies.
How Many Questions are there in Class 12 Maths NCERT Solutions Chapter 6 Application of Derivatives?
Class 12 Maths Chapter 6 Application of Derivatives has 131 questions in 7 exercises. A thorough practice of all these sums ensures concise learning of each topic covered in this lesson. These problems are framed in a specific pattern to promote the understanding of the Application of Derivatives that help students in developing a robust conceptual foundation.
What are the Important Formulas in NCERT Solutions Class 12 Maths Chapter 6?
The important concepts and formulas incorporated in NCERT Solutions Class 12 Maths Chapter 6 are mainly focused on equations of a tangent and normal to a curve at a point, finding turning points on the graph to determine the points where the maximum or minimum values of a function occurs, finding the intervals where a function increases or decreases, approximations, and errors. These concepts are explained in detail with the help of examples and illustrations.
Why Should I Practice NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives?
NCERT Solutions for Class 12 Maths Chapter 6 Application of Derivatives is the best resource for CBSE exam preparation because it covers all the topics as per the latest syllabus. These solutions are designed by a team of highly qualified teachers and subject experts to help students practice various types of questions asked in exams. By practicing these solutions, kids can establish an in-depth understanding of all topics for quick revision during exams.