3.6 a summary of curve sketching greg kelly, hanford high school, richland, washingtonphoto by...
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![Page 1: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/1.jpg)
3.6A Summary of Curve Sketching
Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995
Old Faithful Geyser, Yellowstone National Park
![Page 2: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/2.jpg)
3.6A Summary of Curve Sketching
Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007
Yellowstone Falls, Yellowstone National Park
![Page 3: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/3.jpg)
3.6A Summary of Curve Sketching
Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 2007
Mammoth Hot Springs, Yellowstone National Park
![Page 4: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/4.jpg)
Objective
• Analyze and sketch the graph of a function.
![Page 5: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/5.jpg)
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.
![Page 6: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/6.jpg)
First derivative:
y is positive Curve is increasing.
y is negative Curve is decreasing.
y is zero Possible local maximum or minimum.
Second derivative:
y is positive Curve is concave up.
y is negative Curve is concave down.
y is zero Possible inflection point(where concavity changes).
![Page 7: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/7.jpg)
Analyze the graph of 2
2
2( 9)( )
4
x
f xx
![Page 8: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/8.jpg)
Analyze the graph of 2
2
2( 9)( )
4
x
f xx
![Page 9: 3.6 A Summary of Curve Sketching Greg Kelly, Hanford High School, Richland, WashingtonPhoto by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National](https://reader033.vdocuments.net/reader033/viewer/2022051215/56649e1a5503460f94b07def/html5/thumbnails/9.jpg)
Homework
3.6 (page 208)
#1-5 all
#7 and 9