Calculus Series - Concepts and Formulas™
Differentiation Applications 1 (CLS-CF2)

This sheet provides a comprehensive review of all of the most important topics, concepts and formulas covered in differentiation applications. Each concept is explained in detail, with detailed illustrations. Unlike charts and notes, this Concepts and Formulas™ sheet answers questions about how to use the concepts - how to actually solve problems with them, it doesn't just list facts and formulas. There is even an example, or two, for each concept, to help you to nail down the central ideas.

Topics Covered:

• Implicit functions
• Implicit differentiation
• Differential notation
• Differential formulas
• Related rates
• General guidelines for solving related rates problems
• Geometric interpretation of the derivative
• Secant lines
• Tangents and Normals to the graph of a function
• Slopes of secant and tangent lines
• Difference quotients
• The Nested Interval Theorem
• The Intermediate Value Theorem
• Increasing and Decreasing functions
• Relative maxima and minima
• Absolute maxima and minima
• Critical points
• The Mean Value Theorem
• Rolle's Theorem
• The first derivative test
• The concavity of graphs of functions
• How to test the concavity of a function
• Inflection points
• The second derivative test