Algebra I / Elem. Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems
Algebra II / E&I Algebra
Exponents & Polynomials Intermediate Algebra starts here!

Factoring Rational Expressions Rational Equations and Applications
Algebra III / Inter. Algebra
Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
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
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
Sequences and Infinite Series Power Series Vectors and Geometry of Space Vector-Valued Functions
Calculus IV
15.Functions of Several Variables
16.Multiple Integration
17.Vector Analysis
S = contains supplemental resources
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

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)