Lesson Plan #26
Date: Tuesday November 10th, 2011
Class: AP Calculus
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#26:
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 f and
f ' at x  1?
What is the value of the derivative at all relative
extrema?
What relationship exists between the graph of f and f '
in the interval
1  x  1 ?
What relationship exists between the graph of f and f ' at
x  0?
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
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.
Online Interactive Activity:
Go to
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_as_a_function.html
Have students come up and trace the derivative. Discuss the relationship between the
graph of the function and the graph of the derivative
Online Interactive Activity:
http://www.geogebra.org/en/upload/files/UC_MAT%202009/Brian%20Bisignani/Derivative_Tests.html
Let’s try to establish some relationships between the graph of a function, its first
derivative and its second derivative
Online Interactive Activity:
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_graph_transformation.html
Let’s
.
Online Interactive Activity:
http://webspace.ship.edu/msrenault/GeoGebraCalculus/derivative_first_second.html
If a function is concave up in a certain interval, what could we tell about the graph of
its second derivative?
f is formed from two line
segments and s semicircle
with center at (4,0)
Sample Test Questions: