Lesson 4: 3-4 Differentiating Inverse Trigonometric Functions
Duration of Days: 2
Lesson Objective
Students will be able to Understand the relationship between the derivatives of a function and its inverse.
Students will be able to calculate derivatives of inverse functions.
What is an inverse function, and how is it related to the original function?
What is the geometric relationship between the graphs of a function and its inverse?
How do you determine if a function has an inverse?
What is the derivative of an inverse function, and how is it related to the derivative of the original function?
How does the domain and range of a function relate to the domain and range of its inverse?
C-ID.A.2: Use derivatives to solve problems involving rates of change.
C-ID.A.4: Use derivatives to find the values of a function at a point.
The primary purpose of this unit is to:
Deepen Understanding of Inverse Functions: Reinforce the concept of inverse functions, their domains, and ranges.
Introduce the Inverse Function Theorem: Teach students how to find the derivative of an inverse function at a specific point without explicitly finding the inverse function itself.
Develop Problem-Solving Skills: Apply the Inverse Function Theorem to solve various calculus problems, including those involving logarithmic and trigonometric functions.
Connect to Real-World Applications: Explore real-world contexts where inverse functions and their derivatives are used, such as in economics, physics, and engineering.
DOK 1: Recall and Reproduction
Tasks involve recalling definitions and formulas related to inverse functions and their derivatives.
DOK 2: Skills and Concepts
Tasks require students to apply their knowledge of inverse functions and the Inverse Function Theorem to solve problems.
DOK 3: Strategic Thinking and Reasoning
Tasks demand higher-level thinking skills, such as analyzing, interpreting, and justifying solutions.
DOK 4: Extended Thinking
Tasks require students to synthesize information from multiple sources, make connections, and create original solutions.
Students who finish early will be assigned Prep Test questions to prepare for future assessments.
Students who are struggling with the material will be assigned AP Classroom videos to watch and get additional practice.
College Board AP Classroom Assessments