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: Fun with Reform Calculus

Overview

Reform calculus is a non-traditional way of studying calculus which focused on graphical and numeric approaches instead of algebraic. In a reform calculus course students discover calculus theorems and processes through experimentation rather than having them stated in a textbook. There are some aspects of this approach that are valuable in making one's understanding of the concepts concrete. We'll play with some examples in class.

Objectives

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

• 3.6.1 Gather information about f given the graph of f' or f''.
• 3.6.2 Gather information about f' or f'' given the graph of f
• 3.6.3 Given three graphs determine which is f, f', and f''
• 3.6.4 Graph f given information about the slope of its tangent line, how fast it is increasing/decreasing, etc.

Terminology

Terms you should be able to define: reform calculus, increasing/decreasing most/least rapidly

Mini-Lectures and Examples

rev. 2020-11-07