Latest NCERT Solutions for Class 12 Maths | Chapter 6: Applications of Derivatives | Free PDF Download
NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives
NCERT Solutions for Class 12 Maths | Chapter 6: Applications of Derivatives
Mathematics is one of the most interesting subjects that challenge students to think logically and critically. Among the different topics taught in Mathematics, calculus is one of the most important and complex topics. Calculus is divided into two categories, namely differential calculus and integral calculus. Differential calculus mainly deals with the concepts of derivatives and integrals. Derivatives play a crucial role in determining the rate of change of a function. The concept of derivatives is extensively used in many real-life applications. In this blog, we will discuss NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives.
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Overview of NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives
NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives is one of the most important chapters in Mathematics. This chapter mainly deals with the applications of derivatives in real-life situations. In this chapter, students will learn about the following topics:
- Rate of Change of Quantities
- Increasing and Decreasing Functions
- Tangents and Normals
- Approximations
- Maxima and Minima
All the topics mentioned above are essential for students to understand the applications of derivatives in real-life situations.
Detailed Explanation of NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives:
Rate of Change of Quantities
The concept of rate of change of quantities is essential in determining the speed of change of a quantity. In this section, students will learn how to find the rate of change of a quantity using derivatives. The rate of change of a quantity can be expressed as the derivative of the function representing the quantity.
Increasing and Decreasing Functions
In this section, students will learn how to find out whether a function is increasing or decreasing. If the derivative of a function is positive, then the function is increasing. If the derivative of a function is negative, then the function is decreasing.
Tangents and Normals
In this section, students will learn how to find the equation of a tangent and a normal to a curve at a given point. The equation of a tangent is given by y-y1=m(x-x1), where m is the slope of the tangent and (x1, y1) is the point on the curve. The equation of a normal is given by y-y1=-1/m(x-x1), where m is the slope of the tangent and (x1, y1) is the point on the curve.
Approximations
In this section, students will learn how to find the approximate value of a function using derivatives. The approximate value of a function can be found by using the first-order derivative of the function.
Maxima and Minima
In this section, students will learn how to find the maxima and minima of a function using derivatives. The maximum or minimum value of a function can be found by using the second-order derivative of the function.
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Importance of NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives
NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives is an important chapter as it introduces students to the real-life applications of derivatives. The concepts covered in this chapter are used in many fields, including engineering, physics, economics, and finance. Therefore, it is essential for students to have a clear understanding of the concepts covered in this chapter.
The importance of NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives can be highlighted in the following ways:
- Understanding the Rate of Change: The concept of derivatives is used to calculate the rate of change of a function. This is crucial in various fields such as physics, economics, finance, and engineering. Therefore, students must understand the concept of the rate of change to apply it in practical situations.
- Analyzing Functions: By using derivatives, students can analyze the behavior of functions. They can determine whether a function is increasing or decreasing, find the maximum or minimum value of a function, and approximate the value of a function. This knowledge is essential in many fields such as economics, finance, and engineering.
- Preparing for Competitive Exams: NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives is essential for students who want to appear for competitive exams such as JEE, NEET, and other entrance exams. These exams require a thorough understanding of calculus, and this chapter is a stepping stone towards building that understanding.
Conclusion
In conclusion, NCERT Solutions Class 12 Maths Chapter 6 Applications of Derivatives is an important chapter that introduces students to the applications of derivatives in real-life situations. Students must understand the concepts covered in this chapter to apply them in different fields.
