Maxima and Minima in Calculus: Applications of Derivatives

Finding the absolute highest and lowest values of a function is a cornerstone of calculus that drives decision-making in engineering, economics, and data science. This text-based course guides you through the core principles of optimization, helping you build a strong mathematical intuition for how functions behave. You will transition from basic differentiation to solving complex geometric and real-world optimization problems with confidence. What you'll learn: - Understand the foundational concepts of local and absolute extrema, critical points, and monotonicity. - Apply the First Derivative Test and Second Derivative Test to classify stationary points. - Analyze geometric optimization problems to find maximum areas, minimum volumes, and optimal dimensions. - Solve real-world applied optimization scenarios in business, physics, and data modeling. - Verify mathematical solutions using modern computational thinking and algorithmic step-by-step logic. This comprehensive text-only guide starts with essential terminology, graphical interpretations of slope, and foundational rules of differentiation. You will then progress through structured written examples, step-by-step proofs, and practical optimization scenarios that reinforce each concept. This course is designed for beginners, high school math students, first-year college students, and self-taught learners who have a basic understanding of introductory algebra and fundamental differentiation. No advanced calculus background is required. Start mastering optimization and unlock the practical power of derivatives today.