This course focuses on teaching students about extreme values, the Mean Value Theorem (MVT), increasing/decreasing functions, concavity, and sketching various types of functions. By the end of the course, students will be able to identify absolute and relative extrema, apply the MVT and Rolle's Theorem, determine function behavior using derivatives, and sketch different types of functions. The course uses examples and proofs to explain concepts and is suitable for learners interested in advanced calculus topics.
APEX Calculus - Chapter 3 - Graph Behaviour
Overview
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.
Taught by
Sean Fitzpatrick
