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# Calc04_3 - 4.3 Using Derivatives for Curve Sketching Old...

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4.3 Using Derivatives for Curve Sketching Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 1995 Old Faithful Geyser, Yellowstone National Park

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4.3 Using Derivatives for Curve Sketching Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007 Yellowstone Falls, Yellowstone National Park
4.3 Using Derivatives for Curve Sketching Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2007 Mammoth Hot Springs, Yellowstone National Park

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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.
First derivative: y is positive Curve is rising. y is negative Curve is falling. y is zero Possible local maximum or minimum. Second derivative: y ′′ is positive Curve is concave up.

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Calc04_3 - 4.3 Using Derivatives for Curve Sketching Old...

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