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.



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



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



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



Unit Review

Worksheets




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