📈Graphing📉 functions and their derivatives 🤯🤯 #apcalculus #apcalc #unit5 #shorts

We look at the relationship between a function and its first derivative, investigating how the characteristics of a function's graph relate to its derivative's graph.

We start by exploring the concept of critical points, illustrating how a function's critical points are directly linked to the points where its derivative crosses the horizontal axis. We show scenarios where a function is increasing and how this reflects on its derivative being positive. The derivative's sign changes from negative to positive as the function transitions from decreasing to increasing.

#APCalculus #CalculusTips #MathTutorials #Derivatives #FunctionGraphs

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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Видео 📈Graphing📉 functions and their derivatives 🤯🤯 #apcalculus #apcalc #unit5 #shorts канала Krista King