A Helpful Technique in Calculus and Pre-Calculus: The Sign Pattern

The reason for creating this booklet is to fill a void I have noticed in the majority of introductory calculus and pre-calculus textbooks, over a period of many years. Most basic differential calculus courses traditionally culminate by applying the properties and interpretations of the first and second derivative to problems requiring a sketch of the curve described by the equation, y = f(x). An important part of this solution is dedicated to determining where the curve increases, decreases...