Section 4.3 - Connecting f' and f'' with the Graph of f
Essential Question(s):
Explain how the first and second derivatives are used to analyze the behavior of a function.
Explain how the first and second derivatives are used to analyze the behavior of a function.
Follow these three steps to complete this "flip" lesson.
STEP 1: Preparation
Title your spiral with the heading above and copy the essential question(s).
Title your spiral with the heading above and copy the essential question(s).
STEP 2: Vocabulary & Examples
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your Cornell notes.
Copy and define the following of vocabulary. This can be any tables, properties, theorems, terms, phrases or postulates listed. Review the following examples and copy what is necessary for you. Use the guiding questions for your Cornell notes.
First Derivative Test for Local Extrema
Concavity
Points of Inflection
Second Derivative Test for Local Extrema
Learning About Functions from Derivative
Concavity
- What is concavity?
- What is the concavity test?
Points of Inflection
- What is a point of inflection?
- What are some cautions when using the second derivative for points of inflection?
Second Derivative Test for Local Extrema
- What is the second derivative test for local extrema?
Learning About Functions from Derivative
- Summary of what we can learn from first and second derivatives.
STEP 3: Reading
If time permits, reread the lesson and take any extra notes as needed.
If time permits, reread the lesson and take any extra notes as needed.
