Applications of Differential Calculus — Class 12 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 12 Mathematics, Chapter 7. Tangents, normals, maxima/minima and curve sketching.
1. About this chapter
This chapter covers Applications of Differential Calculus as part of the Class 12 Samacheer Kalvi Mathematics curriculum. It deals with tangents, normals, maxima/minima and curve sketching and builds conceptual understanding essential for the TN HSC Public Exam.
By the end of this chapter, students will be able to:
- Find equations of tangents and normals to curves
- Apply first and second derivative tests for extrema
2. Key concepts
- Concept 1: Find equations of tangents and normals to curves.
- Concept 2: Apply first and second derivative tests for extrema.
3. Important terms and formulas
| Term / Formula | Description |
|---|---|
| Find equations of tangents… | Find equations of tangents and normals to curves |
| Apply first and second… | Apply first and second derivative tests for extrema |
4. Worked examples
Example 1. Applying a key concept from this chapter.
Solution: Identify the relevant principle → apply the formula or rule → state the answer with correct units.
Example 2. A typical exam-style question on applications of differential calculus.
Solution: Break the problem into steps, use the appropriate formula and verify the answer.
5. Common mistakes
- Mistake: Skipping units or forgetting to state them. Fix: Always write units alongside every quantity and answer.
- Mistake: Confusing similar terms or concepts in this chapter. Fix: Make a comparison table of the terms during revision.
6. Practice (exam-style)
- Define the main term or principle covered in Chapter 7.
- Give two real-life examples related to applications of differential calculus.
- Solve a short numerical or descriptive question from this chapter.
- State one important formula and explain each symbol.
7. Answer key (hints)
- Refer to section 2 (Key concepts) above for the definition.
- Examples should be drawn from daily experience and local context.
- Apply the formula from section 3, show all steps clearly.
- Formula with units — refer to the textbook glossary for symbol meanings.
8. Quick revision
- Class 12 Mathematics — Chapter 7: Applications of Differential Calculus.
- Core idea: Tangents, normals, maxima/minima and curve sketching.
- Key outcomes: Find equations of tangents and normals to curves; Apply first and second derivative tests for extrema.
- Always revise diagrams / tables from the Samacheer Kalvi textbook before the exam.
