Unit Objective:

Learn to use the derivatives of a
function to sketch its graph. Be able to find and use asymptotes when sketching the graph of a
rational function. Be able to find minimums and maximums. Be able to find differentials and use
them to approximate change. This unit should take no more than 2 weeks to complete.

*All assignments are in Basic Technical Mathematics With Calculus 7th edition
by Allyn J. Washington, 2000.

Method of Evaluation:

The unit test will be a pencil and paper quiz taken at your class site. The test will be
administered by the instructor or by a proctor. Please see the course schedule for the exact
time and date of the unit test.

Objective One

Be able to use the first derivative to determine where a curve is increasing or decreasing.
Find critical values and relative extrema.

- Read 24.5, pages 690-692.
- Complete Work Exercises 24.5, page 695 #1-7 odd.
**Quick Review sheet 4-1**.

Objective Two

Be able to use the second derivative to determine where a graph is concave up, concave down,
or has an inflection point. Be able to sketch a graph using critical points and above information.
Understand second derivative test.

- Read 24.5, pages 693-694.
- Complete Work Exercises 24.5, page 695 #9-27 odd, 31-37 odd, 38-40 all

(#29 if graphing calculator). **Quick Review sheet 4-2**.

Objective Three

Be able to find vertical and horizontal asymptotes and sketch rational functions.

- Read 24.6, pages 696-699, Example 1 and 4.
- Complete Work Exercises 24.6, page 699 #3,11,17,19.
**Quick Review sheet 4-3**.

Objective Four

Be able to solve minimum and maximum applications using derivatives. Be able to use the
second derivative test.

- Read 24.7, pages 700-704.
- Complete Work Exercises 24.7, pages 704-706 #1-7 odd, 6,8,11,12,13,19,20,21,23,26,29,31.
**Quick Review sheet 4-4**.

Objective Five

Learn the definition and
meaning of differentials and use them to approximate .

- Read 24.8, pages 706-709.
- Complete Work Exercises 24.8, page 710 #9-25 odd, 29,31.
**Quick Review sheet 4-5**.

Unit Review

- Review Exercises, page 711 #17-23 odd, 47,53,61,63.
- Practice Test, page 714 #4,7,8,10.

Worksheets

- Objective 1a Worksheet.
- Objective 1b Worksheet.
- Objective 2a Worksheet.
- Objective 2b Worksheet.
- Objective 2c Worksheet.
- Objective 3 Worksheet.
- Objective 4 Worksheet.
- Objective 5 Worksheet.
- Answers.