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, 1995 Yellowstone Falls, Yellowstone National Park
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In the past, one of the important uses of derivatives was as an aid in curve sketching. We usually use a calculator of computer to draw complicated graphs, it is still important to understand the relationships between derivatives and graphs.
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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. y ′′ is negative Curve is concave down. y ′′ is zero Possible inflection point (where concavity changes).
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Example: Graph ( 29 ( 29 2 3 2 3 4 1 2 y x x x x = - + = + - There are roots at and . 1
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Calc04_3 - 4.3 Using Derivatives for Curve Sketching Old...

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