Core Calculus: Understanding Maxima and Minima

Maxima and Minima are essential concepts in calculus, providing the tools needed to understand the behavior of functions and solve fundamental optimization challenges across science and engineering. By the end of this course, you will be able to confidently use differentiation techniques to locate critical points, determine whether they represent local maximums or minimums, and apply these methods to solve practical problems requiring the maximization or minimization of quantities. What you'll learn: * Understand the geometric and algebraic definitions of local and global extrema. * Learn to use the first and second derivative tests to accurately identify critical points and points of inflection. * Apply concepts of differentiation to analyze function behavior, including increasing/decreasing intervals and concavity. * Practice solving classic optimization word problems involving geometric shapes, economics, and physical constraints. * Configure simple optimization models for basic engineering or data science scenarios. The course begins by establishing the necessary foundational definitions of differential calculus, progresses through the standard testing methods for extrema, and concludes with extensive practice applying these techniques to solve real-world optimization exercises. This course is designed for absolute beginners in calculus, students preparing for foundational STEM subjects, or anyone needing a strong grasp of function analysis and optimization. No prior calculus knowledge is required. Start reading today and build a solid foundation in core calculus analysis.