Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III

Course: Calculus I
Topic: Analysis of Curves
Subtopic: Curve Sketching

Overview

The goal today is to pull all the information obtained from the first and second derivatives including CPs, IPs, relative extrema, increasing/decreasing, concavity, etc. together and use it to accurately sketch the function "by hand".

Objectives

By the end of this topic you should know and be prepared to be tested on:

• 3.5.1 Review skills listed in Lesson Notes 1.8 to be sure that you can use limits at infinity to find horizontal asymptotes
• 3.5.2 Use information about a function obtained from the 1st and 2nd derivative (CPs, IPs, increasing/decreasing, concavity, etc.) to sketch the function manually

Mini-Lectures and Examples

Supplementary Resources (recommended)

My Template for Curve Sketching can be used to compile all the information about a function obtained from f, f', and f'' so that it can be sketched and analyzed.

Supplementary Resources (optional)

Examples: Calculus: Applications of the Derivative - Asymptotes from Math24 has lots of interesting examples of using limits to find asymptotes.

rev. 2020-11-07