Solution videos for the Applications of Derivatives problem set are below (note that you do not need to complete 1991 AB1). These problems review all of the ideas we have been working with except for Rolle's Theorem and the Mean Value Theorem. I will post examples of those as well before the test. Study these!!! :)

I have fixed the sound issues on 1993 AB1 and 1992 AB1.

Applications of Derivatives Problem Set (printable)
Applications of Derivatives Problem Set Solutions (printable)

1996 AB1 Video #1
1996 AB1 Video #2
1996 AB1 Video #3

1994 AB1 Video #1
1994 AB1 Video #2
1994 AB1 Video #3

1993 AB4 Video #1
1993 AB4 Video #2
1993 AB4 Video #3

1993 AB1 Video #1
1993 AB1 Video #2

1992 AB1 Video #1
1992 AB1 Video #2

1991 AB5 Video #1
1991 AB5 Video #2
1991 AB5 Video #3

First, I have included the posters from the classroom that are relevant to our current topics. These posters cover all of the major concepts that we are working with on this upcoming test. In the next blog post, I will provide some examples that utilize these ideas.

Summary of Curve Sketching

Larson 7.0 Chapter 3 Section 6 #7-37 odds

Concavity / Points of Inflection

For Monday night Larson 7 Ch 3 Section 4 #11-25 odds
For Tuesday night Larson 7 Ch 3 Section 4 #27-39

Intervals of Increasing/Decreasing, Relative Min/Max

The first graphic shows the relationship between a function's behavior and it's first derivative and also the steps to identify the intervals of increasing/decreasing.



The second graphic states the First Derivative Test which tells us whether the function has a relative minimum, relative maximum or neither at each critical number.



The third graphic shows an example of finding intervals of increasing and decreasing in a function and makes use of the First Derivative Test to draw conclusions about relative minimums and maximums. Our notation is handwritten below. You can feel free to use any notation that works for you. In the end though, you must state specifically any conclusions you draw from the sign chart.



Please complete 11-35 odds for Monday. Thanks and enjoy your blizzard!

Mean Value Theorem

Remember the steps:
1) Verify that the function is continuous on the closed interval and differentiable on the open interval. If not, stop here. You wish you could be so lucky :)
2) Find the derivative
3) Find the slope of the secant line connecting the end points
4) Set 1 and 2 equal to eachother
5) Solve for x (which is c in this case)
6) Use only the values of x that lie WITHIN the interval (don't include end points here)

Complete 31-41 odds

Rolle's Theorem

Below is the definition of Rolle's Theorem.



Remember the steps:
1) Verify that the function is continuous on the closed interval and differentiable on the open interval. If not, stop here. You wish you were so lucky :)
2) Find the derivative
3) Set the derivative equal to 0
4) Solve for x (in this case it is c)
5) Use only the values of x that lie WITHIN the interval (don't include end points here)

Complete the odd problems for homework. Solutions are in the online book.