Application of Derivatives (Monotonicity)

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About Course

Course Description:

Monotonicity is a fundamental concept in mathematics that plays a crucial role in various mathematical disciplines, including calculus and real analysis. This course is designed for Class 12 students and those preparing for the Indian Institute of Technology Joint Entrance Examination (IIT JEE). It aims to provide a comprehensive understanding of monotonicity, its applications, and its significance in solving mathematical problems.

Course Objectives:

  1. To introduce students to the concept of monotonic functions.
  2. To explain the properties of increasing and decreasing functions.
  3. To teach techniques for determining the monotonicity of functions.
  4. To explore the role of monotonicity in calculus and mathematical analysis.
  5. To solve practical problems involving monotonic functions.
  6. To prepare students for competitive examinations like IIT JEE.

By the end of this course, students will have a solid understanding of monotonicity and its applications, which will not only help them excel in their Class 12 mathematics curriculum but also prepare them for the challenges of competitive exams like IIT JEE.

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What Will You Learn?

  • Definition of Monotonicity: Understand what monotonicity means in mathematics and how it applies to functions.
  • Types of Monotonicity: Learn about different types of monotonicity, including strictly increasing, strictly decreasing, non-decreasing, and non-increasing functions.
  • Determining Monotonicity: Discover techniques for analyzing and determining whether a function is monotonic, including the use of derivatives and critical points.
  • Applications in Calculus: Explore how monotonicity is used in calculus, including its role in the Fundamental Theorem of Calculus, the Mean Value Theorem, and integral calculus.
  • Real-World Applications: Understand how monotonicity is applied to solve practical problems in various fields such as physics, economics, and engineering.
  • Preparation for Competitive Exams: Gain insights into strategies and techniques for solving problems related to monotonicity in competitive exams like IIT JEE.

Course Content

Increasing and Decreasing Functions

  • Increasing and decreasing functions at a point
  • Monotonicity in an Interval
  • Examples on Monotonicity P1
  • Examples on Monotonicity P2
  • Examples on Monotonicity P3

Least and Greatest Values of Functions

Establishing Inequalities

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