1. 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National Park

2. 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007 Yellowstone Falls, Yellowstone National Park

3. 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007 Mammoth Hot Springs, Yellowstone National Park

4. Objective Analyze and sketch the graph of a function.

5. In the past, one of the important uses of derivatives was as an aid in curve sketching. Even though we usually use a calculator or computer to draw complicated graphs, it is still important to understand the relationships between derivatives and graphs.

6. First derivative: is positive Curve is increasing. is negative Curve is decreasing. is zero Possible local maximum or minimum. Second derivative: is positive Curve is concave up. is negative Curve is concave down. is zero Possible inflection point (where concavity changes).

7. Analyze the graph of

9. Homework 3.6 (page 208) #1-5 all #7 and 9