Calculus 4.3

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3.6 A Summary of Curve Sketching
Old Faithful Geyser, Yellowstone National Park
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3.6 A Summary of Curve Sketching
Yellowstone Falls, Yellowstone National Park
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3.6 A Summary of Curve Sketching
Mammoth Hot Springs, Yellowstone National Park
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Objective

• Analyze and sketch the graph of a function.

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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.
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First derivative
Curve is increasing.
Curve is decreasing.
Possible local maximum or minimum.
Second derivative
Curve is concave up.
Curve is concave down.
Possible inflection point (where concavity
changes).
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Analyze the graph of
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Analyze the graph of
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Homework

• 3.6 (page 208)
• 1-5 all
• 7 and 9