Mastering Derivatives: A Complete Calculus Course

• Rationalization
• Basic Concept of Limits
• Rates of Change
• The Definition of Derivative
• Derivative of Polynomial Functions
• The Product Rule
• The Quotient Rule
• The Chain Rule
• Higher Order Derivative
• Maximum/Minimum in an Interval
• Optimization
• Critical Point, Interval of Increasing/Decreasing
• First Derivative Test to determine Maximum/Minimum
• Vertical and Horizontal Asymptote
• Point of Inflection, Concavity
• Curve Sketching
• Derivative of Exponential Functions
• Derivative of Trigonometric Functions

This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modeling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra