Going the Distance...Going for Speed (Calculus)

Introduction

Understanding how things move, whether designing a thrilling (but safe) water slide or the world’s most complicated Rube Goldberg machine, is critical for success.  Dive into the world of derivatives to see how calculus drives motion in our world.

Essential Questions

• How are derivatives defined and calculated in functions?
• Why would the chain, product, or quotient rule be chosen for use in finding a derivative of a particular function?
• How is differentiation used to solve various kinds of problems?
• Why are derivatives helpful in solving optimization and related rates problems?
• What is the Mean Value Theorem and how can it be applied in real-world scenarios?

Learning Objectives

Students will be able to…

• Derivatives of Exponential Functions

• Derivatives of Inverse Trigonometric Functions

• Derivatives of Logarithmic Functions

• Derivatives of Polynomials

• Derivatives of Radical Functions

• Derivatives of Rational Functions

• Derivatives of Trigonometric Functions

• Finding Derivatives Using the Chain Rule

• Finding Derivatives Using the Product Rule

• Finding Derivatives Using the Quotient Rule

• Extreme Value Theorem

• L’Hospital’s Rule

• Local Linearity and Approximation

• Mean Value Theorem

• Solving Optimization Problems

• Solving Related Rates Problems

• Using Differentiation to Solve Motion Problems