Chapter 6 of the NCERT Class 12 Maths textbook is Application of Derivatives, and it is one of the most practical and useful chapters in the entire calculus section. This chapter teaches how to use derivatives in real-world mathematical problems like finding the rate of change, increasing or decreasing functions, maxima and minima, tangents and normals, and more. The PDF version of this chapter is available for free on the official NCERT website, and it’s highly recommended for students to keep a digital copy for quick revision and practice.
I’ve chosen to write about this chapter because I’ve seen many students who understand how to differentiate but get confused when it comes to applying those concepts. I remember struggling with word problems involving speed, slope, and finding the highest or lowest value of a function. But once I understood what each formula meant and where to apply it, things became easier. This chapter is important not just for CBSE board exams but also for JEE, NDA, CUET, and other competitive exams. If you understand this chapter well, you can handle a lot of real-life situations in physics, economics, and engineering. That’s why I think it’s important to break it down properly and also share how to download the official NCERT PDF.
What You Will Learn in Chapter 6: Application of Derivatives
This chapter focuses on using the concept of derivatives to solve different types of problems. Here’s what it covers:
- Rate of Change of Quantities
- How fast one quantity changes with respect to another
- Useful in physics problems and real-world applications
- Increasing and Decreasing Functions
- Finding intervals where the function increases or decreases
- Using first derivative to analyse function behaviour
- Tangents and Normals
- Finding the equation of the tangent or normal at a given point
- Very helpful in geometry and coordinate-based problems
- Maxima and Minima
- Identifying the maximum or minimum value of a function
- Includes first and second derivative tests
- Application in Word Problems
- Real-life scenarios involving optimisation
- Includes problems on least cost, maximum area, minimum time, etc.
These topics are all explained clearly in the NCERT textbook with step-by-step examples and diagrams. Many of the exercise questions are based on board exam patterns.
Example:
Find the point on the curve
y = x² + 1
where the tangent is parallel to the line y = 2x + 3.
Here, you’ll differentiate, equate the slopes, and solve for x — this is a common type of board-level question.
Why This Chapter Is So Important
Application of Derivatives is the chapter where mathematics really starts to feel useful. All the rules you learned in the previous chapters come together here. Whether you want to analyse motion, optimise cost or profit, or solve geometric problems, this chapter helps you build that skill. It’s a mix of logic, formulas, and interpretation.
In the CBSE board exam, you can expect one 5- or 6-mark question directly from this chapter. In JEE Main, questions on increasing/decreasing functions and optimisation appear frequently. Even in CUET and NDA, this chapter is tested regularly. If you want to score high in calculus, you cannot skip this chapter. Once you understand the basic pattern of the questions, solving them becomes much easier with practice.
Download NCERT Class 12 Maths Chapter 6 PDF
Here’s how you can download the official and latest PDF of Chapter 6
