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:

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f is formed from two line segments and s semicircle with center at (4,0)

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