Calculus Basics: Tangents, Normals, and Function Behavior

Understanding how functions change and bend is the cornerstone of calculus. This course breaks down the core applications of derivatives, showing you exactly how to determine where functions rise or fall and how to find the equations of tangent and normal lines. By mastering these concepts, you will transition from simply calculating derivatives to confidently analyzing the geometric behavior of complex curves. What you'll learn: - Understand the fundamental geometric meaning of derivatives, tangents, and normals. - Calculate the precise equations of tangent and normal lines to any curve at a given point. - Analyze intervals where functions are strictly increasing or decreasing using first derivative tests. - Identify critical points and turning points to understand function behavior. - Explore how these rate-of-change concepts are applied in modern data analysis and optimization algorithms. This course begins with foundational definitions and key terminology before moving into step-by-step mathematical proofs and practical problem-solving. Through clear written explanations and structured practice exercises, you will build a strong intuitive and algebraic grasp of calculus. This course is designed for beginners, high school mathematics students, and anyone preparing for exams that require a solid foundation in calculus. Start mastering the behavior of curves today.