In this unit, are back in abstract land where the problems don’t have some context like Paul needing to buy 5 apples, but that means there is a focus on understanding abstract structures of problems and writing good formal conclusions for how a problem works. With this, you must justify your answer for solutions and “apply abstract reasoning skills to justify solutions for realistic optimization problems”.
Topics
- Using the Mean Value Theorem
- Extreme Value Theorem, Global vs Local Extrema and Critical Points
- Determining intervals on which a function is increasing or decreasing
- Using the First Derivative Test to Determine Relative Extrema
- Using the Candidates test to Determine Absolute Extrema
- Determining concavity of functions of their domains
- Using the second derivative test to determine extrema
- Sketching Graphs of Functions and Their Derivatives
- Connecting a Function, it’s first derivative and it’s second derivative
- Introduction to Optimization Problems
- Solving Optimization Problems
- Exploring Behaviors of Implicit Relations