Lesson 3: 4.3 How Derivatives Affect the Shape of a Graph
Duration of Days: 3
Lesson Objective
Determine information about the graph of a function, such as intervals of increasing/decreasing, local and absolute max and mins, intervals of concavity, and inflection points, based on first and second derivatives of the function.
- Where is a function increasing? Decreasing?
- Where does a function have local and/or absolute maximum or minimum values?
- Where is a function concave up? Concave down?
- Where does a function have inflection points?
- increasing/decreasing test
- first derivative test
- concavity (upward or downward)
- inflection point
- concavity test
- second derivative test
(Properties of graphs of functions based on derivatives of the function)
- Determine properties of the graph of a function using information from the first and second derivatives of the function
- DOK levels 1-4
- analyzing financial market acceleration
- modeling disease spread
- behavior of suspension systems and springs
At this point, students are proficient with finding derivatives. Sometimes they may confuse what information we get from first versus second derivatives.
Homogeneous grouping and whole class discussion
section assessment
problems assigned from book, business revenue data