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How are derivatives used to help analyze and graph a function or to solve optimization problems?
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Student Learning Map
- Topic:Applications of Derivatives
- Subject(s):Math
- Days:30
- Grade(s):11, 12
Key Learning:
To use the derivatives to find slope and tangent lines, and to analyze and graph functions, finding intervals of change and concavity.
Unit Essential Question(s):
Concept: Graph Sketching and Analysis Lesson Essential Question(s):How is the derivative used to find the maximum and minimum points of a function? (A)Why is it useful to be able to calculate the extreme values of functions and what are some real-life applications? (ET)Lesson Essential Question(s):How is the first derivative used to find where a function is increasing or decreasing? (A)How is the second derivative used to determine the concavity of a function at various intervals? (A)What are the graphical relationships between a function, its first derivative, and its second derivative? (A)What are the graphical relationships between a function, its first derivative, and its second derivative? (ET)Vocabulary:Vocabulary:Vocabulary:
Additional Info:
Calculus textbook Graphing Calculator TI-Presenter Ancillary material
Resources:
Acquisition Lesson(s):
1. How is the derivative used to find the maximum and minimum points of a function?2. How is the first derivative used to find where a function is increasing or decreasing?3. How are first and second derivatives used to solve modeling, optimization and related rate problems?4. How is the second derivative used to determine the concavity of a function at various intervals?5. What are the graphical relationships between a function, its first derivative, and its second derivative?Extended Thinking Lesson(s):
1. How are first and second derivatives used to solve modeling, optimization and related rate problems?2. Why is it useful to be able to calculate the extreme values of functions and what are some real-life applications?3. What are the graphical relationships between a function, its first derivative, and its second derivative?