NCERT Solutions for Class 12 Maths Chapter 5 Exercise 5.7 Continuity and Differentiability - PDF Download

NCERT solutions for class 12 maths chapter 5 exercise 5.7 Continuity and Differentiability focuses on second-order derivatives and related concepts. The second derivative, also known as the second-order derivative in calculus, is useful for calculating the rate of change of a quantity to itself. Ex 5.6 class 12 maths chapter 5 is a great way to assist students in applying a variety of methods to determine the second-order derivatives of various function types.

Class 12 maths chapter 5 exercise 5.7 NCERT solutions consist of 17 questions based on derivatives. You can solve all the questions of exercise 5.7 with the help of NCERT solutions of ex 5.7 class 12 maths chapter 5 provided by the academic team of mathematics. Ex 5.7 class 12 maths ch 5 NCERT solution has explained the concept of second order derivatives to prepare for board exams. Class 12 maths chapter 5 exercise 5.7 NCERT solutions are also provided here in PDF format. You can download the free PDF of these solutions from the official website of eSaral and practice questions anytime. 

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Topics Covered in Exercise 5.7 Class 12 Mathematics Questions

Ex 5.7 class 12 maths chapter 5 covers the topic of second order derivatives. Students can check below the detailed explanation of this topic.

1.  Second Order Derivative

The derivative of the function's first derivative is known as the second order derivative. We can determine the instantaneous rate of change of a function at a particular position or the slope of the tangent at that place using the first-order derivative at that point. We can get an understanding of the shape of a graph for a particular function using the Second-Order Derivative. The second order derivative of f(x) is denoted by f″(x). It is also denoted by D² y or y″ or y₂ if y = f(x).

Let y = f(x). Then 

$\frac{d y}{d x}=f^{\prime}(x)$      ……(1)

If f′(x) is differentiable, we may differentiate (1) again w.r.t. x. Then, the left hand side becomes $\frac{d}{d x}\left(\frac{d y}{d x}\right)$ which is called the second order derivative of y w.r.t. x and is denoted by $\frac{d^2 y}{d x^2}$

Tips for Solving Exercise 5.7 Class 12 Chapter 5 Continuity and Differentiability

Our subject experts of eSaral have provided some useful tips to solve exercise 5.7 class 12 maths chapter 5.

1. While solving ex 5.7 class 12 maths NCERT solutions, students should remember that practicing examples is more important than just reading theory when they are preparing for board exams.
2. To acquire a more practical approach, you should also practice the important sums that are included in these solutions.
3. To prevent even the smallest errors, students must carefully follow each step of the solution.
4. Students will gain the necessary understanding of second-order derivatives and their representation after closely reading the mathematical equations and solutions. 
   

Importance of Solving Ex 5.7 Class 12 Maths Chapter 5 Continuity and Differentiability

There are numerous benefits of solving ex 5.7 class 12 maths chapter 5. 

1. Second order derivatives included in exercise 5.7 have been described in detail by the expert teachers of eSaral that will help you to understand the nature of each question.
2. All the questions of ex 5.7 class 12 maths are solved in step by step manner which gives you clear and precise knowledge of concepts.
3. By practicing ex 5.7 class 12 maths chapter 5 in NCERT solutions will boost your self-confidence to solve questions in board exams.
4. NCERT solution PDFs provide accurate answers to all the questions of ex 5.7 that will help you to cross check your answers.

Frequently Asked Questions

Question 1. Is it easy to find second-order derivatives?

Since a function's second-order derivative can only be found after its first-order derivative has been determined, finding a function's second-order derivative requires knowledge of how to find its first-order derivative. Using the same techniques, you can find the second-order derivative after you have the first-order derivative. Finding both derivatives will be simpler for you if you are familiar with the fundamentals of differentiation.

Question 2. What is the representation for the second derivative?

If y = f(x). Then $\frac{d y}{d x}$= f ′(x) If f ′(x) is differentiable, we may differentiate $\frac{d y}{d x}$ again w.r.t. x. Then, the left hand side becomes $\frac{d}{d x}\left(\frac{d y}{d x}\right)$ which is called the second order derivative of y w.r.t. x and is denoted by $\frac{d^2 y}{d x^2}$ The second order derivative of f(x) is denoted by f″(x). It is also denoted by D² y or y″ or y₂ if y = f(x).