APEX Calculus - Chapter 3 - Graph Behaviour

Overview

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Dive into a comprehensive 3.5-hour video series on graph behavior in calculus, covering extreme values, the Mean Value Theorem, increasing and decreasing functions, concavity, and graph sketching. Explore absolute and relative extrema, critical points, Rolle's Theorem, and the First and Second Derivative Tests. Learn to analyze various function types, including polynomials, rational functions, trigonometric functions, and those with fractional powers. Apply these concepts through numerous examples to enhance your understanding of function behavior and graphing techniques.

Syllabus

Graphs: Extreme Values - 01. Absolute extrema.
Graphs: Extreme Values - 02. EVT.
Graphs: Extreme Values - 03. Relative extrema.
Graphs: Extreme Values - 04. Critical Points.
Graphs: Extreme Values - 05. Example.
Graphs: Extreme Values - 06. Example.
Graphs: Extreme Values - 07. Example.
Graphs: MVT - 01. Intro.
Graphs: MVT - 02. Rolle's Theorem.
Graphs: MVT - 03. Example.
Graphs: MVT - 04. Proof of MVT.
Graphs: MVT - 05. Function with derivative zero is constant.
Graphs: MVT - 06. Functions with equal derivatives differ by a constant.
Graphs: MVT - 07. Example.
Graphs: MVT - 08. Example.
Graphs: Increasing/Decreasing - 01. Definition.
Graphs: Increasing/Decreasing - 02. Role of Derivative Sign.
Graphs: Increasing/Decreasing - 03. Example.
Graphs: Increasing/Decreasing - 04. First Derivative Test.
Graphs: Increasing/Decreasing - 05. Example.
Graphs: Increasing/Decreasing - 06. Example.
Graphs: Concavity - 01. Intro.
Graphs: Concavity - 02. Example.
Graphs: Concavity - 03. Example.
Graphs: Concavity - 04. Example.
Graphs: Concavity - 05. Second Derivative Test.
Graphs: Concavity - 06. Example.
Graphs: Sketching - 01. Polynomial.
Graphs: Sketching - 02. Rational.
Graphs: Sketching - 03. Polynomial (Factored).
Graphs: Sketching - 04. Trig.
Graphs: Sketching - 05. Fractional powers.