Скачать или смотреть 📍Local📍 vs. 🌎global🌎 extrema on an interval

We look at the difference between local and global extrema, also known as relative and absolute extrema, when we're considering an interval (a,b). For a function that's continuous over an interval from a to b, it's guaranteed that the function will achieve both its highest and lowest values at least once within this interval. This principle lays the foundation for identifying the extrema of functions in specified ranges.

We highlight how a function can have both a local maximum and minimum within an interval, marking the highest and lowest points in localized regions. However, it's crucial to note that when these points are compared with the interval's endpoints, the absolute extrema (the highest and lowest values in the entire interval) might be located at different points.

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Unit 5 of AP Calculus is all about Analytical Applications of Differentiation:
5.1 Using the Mean Value Theorem
5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
5.3 Determining Intervals on Which a Function Is Increasing or Decreasing
5.4 Using the First Derivative Test to Determine Relative (Local) Extrema
5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
5.6 Determining Concavity of Functions over Their Domains
5.7 Using the Second Derivative Test to Determine Extrema
5.8 Sketching Graphs of Functions and Their Derivatives
5.9 Connecting a Function, Its First Derivative, and Its Second Derivative
5.10 Introduction to Optimization Problems
5.11 Solving Optimization Problems
5.12 Exploring Behaviors of Implicit Relations

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