Class: AP Calculus
Lesson Plan #76
Class: PreCalculus Date: Thursday April 16th, 2015
Topic: Analysis of the graphs of functions and its derivative.
Aim: How can we interpret the graphs of the derivatives of functions?
Objectives:
1) Students will be able interpret graphs of the derivatives of functions
HW#76:
Do Now:
At right you have the graph of a function shown in the solid line and graph of the derivative shown as a dotted line.
What relationship exists between the graph of [pic]and [pic]at [pic]?
What is the value of the derivative at all relative extrema?
What relationship exists between the graph of [pic]and [pic] in the interval [pic]?
What relationship exists between the graph of [pic]and [pic]at [pic]?
Questions:
If a function is increasing, what can we tell about the derivative?
If a function is decreasing, what can we tell about the derivative?
At a relative extreme value in the function, what can you tell about the value of the derivative?
At a point of inflection in the function, what happens in the derivative?
PROCEDURE:
Write the Aim and Do Now
Get students working!
Take attendance
Go over the HW
Collect HW
Go over the Do Now
[pic]Hands on Activity:
We are going to work with a program called Geogebra that will help us discover the relationships that exist between the graph of a function and the graph of its derivative and the graph of its second derivative.
After generating graph of function and setting up the trace of the derivative, have a student come up and trace the derivative. Discuss relationships between the graph of the function and the graph of the derivative.
[pic] Online Interactive Activity:
Go to
Have students come up and trace the derivative. Discuss the relationship between the graph of the function and the graph of the derivative
[pic] Online Interactive Activity:
Let’s try to establish some relationships between the graph of a function, its first derivative and its second derivative
[pic] Online Interactive Activity:
Let’s
.
[pic] Online Interactive Activity:
If a function is concave up in a certain interval, what could we tell about the graph of its second derivative?
Sample Test Questions:
-----------------------
f is formed from two line segments and s semicircle with center at (4,0)
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