Unit Four

# Curve Sketching and Min/Max

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.

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.

• 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.

• 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 .

Unit Review

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

Worksheets