Big Picture / We are in the middle of our CALC unit and now have some very useful calculus tools to work with. It is now that we begin our application side of this subject. But before we do that we need to do some final graphical analysis using our calc tools.
Context of this Lessons / Today we will look at the story that the first and second derivative tell use about the graph of a function.
To Do Today!
IB SL 2 - Lesson 9.9: Graphical Analysis / Unit 9: Derivative Calculus-Task 0:Warm Up
-Task 1:Increasing and Decreasing
-Task 2:Two Examples
-Task 3: General Notes
-Task 4: Stationary Points
-Task 5: Concavity and Inflection
IB SL 2 - Lesson 9.9: Graphical Analysis / Unit 9: Derivative CalculusTask 0: Recap Notes
IB SL 2 - Lesson 9.9: Graphical Analysis / Unit 9: Derivative CalculusA particle moves along a line with displacement functions .
- Write an expression for the velocity of the particle at time t.
- Hence, find when the particle is at rest.
- Write an expression for the acceleration of the particle at time t.
- Hence show that the velocity is never decreasing.
Task 1:Intervals of increasing and decreasing
Task 2: Two Examples
Use the derivative of f to find the intervals on which f is increasing or decreasing…
-Step 1: Find the
-Step 2: Find the
-Step 3: Interpret the Derivative for sign… or make a sign diagram
-Step 4: Use interval notation to describe the intervals.
a.
b.
c.
Task 3: General notes and Vocabulary
Task 4: Classifying “Stationary Points”
a.
b.
c.
Task 5:Concavity and Points of Inflection
Use the second derivative to determine intervals when the function is concave up and concave down. Find any points of inflection.
a.
b.
c.