Application of Derivatives (Tangent and Normal)

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About Course

Course Description:

The course on Tangent and Normal is designed for Class 12 students and individuals preparing for the Indian Institute of Technology Joint Entrance Examination (IIT JEE). This course delves into the fundamental concepts of tangent lines and normal lines to curves, emphasizing their significance in calculus, geometry, and real-world applications. Through this course, students will develop a deep understanding of tangent and normal lines, enabling them to tackle complex problems with confidence.

Course Objectives:

  1. To introduce students to the concepts of tangent and normal lines.
  2. To explain the geometric interpretation of tangents and normals.
  3. To teach techniques for finding tangent and normal lines to curves.
  4. To explore the role of tangents and normals in calculus, including derivatives.
  5. To solve practical problems involving tangent and normal lines.
  6. To prepare students for competitive examinations like IIT JEE

By the end of this course, students will have a solid grasp of tangent and normal lines, enabling them to tackle complex mathematical problems and excel in their Class 12 mathematics curriculum and competitive examinations like IIT JEE.

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What Will You Learn?

  • Tangent Line Concepts: Understand the definition and geometric interpretation of tangent lines to curves, including their significance in describing instantaneous rates of change.
  • Finding Tangent Lines: Learn techniques for finding the equation of the tangent line at a given point on a curve, including parametric and polar curves.
  • Normal Line Concepts: Explore the concept of normal lines and their relationship with tangent lines, including techniques for finding the equation of the normal line at a given point.
  • Tangents and Derivatives: Understand the deep connection between tangent lines and derivatives, including how derivatives represent slopes of tangent lines.
  • Applications in Geometry and Physics: Discover practical applications of tangent and normal lines in geometry, kinematics, engineering, and physics.
  • IIT JEE Preparation: Gain strategies and problem-solving skills specifically tailored to tackling IIT JEE questions related to tangents and normals.

Course Content

Introduction to Tangent and Normals

  • Definition of Tangent and Normal
  • Examples on Tangent and Normal P1
  • Examples on Tangent and Normal P2
  • Examples on Tangent and Normal P3
  • Important Notes on Tangent and Normal

Intersection of Two Curves

Length of Tangent and Normals

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