Curve Sketching

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Curve Sketching

• Section 3.6

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DISAIMIS
OMAIN
NTERCEPTS
YMMETRY
SYMPTOTES
NTERVALS
AX MIN
NFLECTION
KETCH
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DISAIMIS
OMAIN
NTERCEPTS
YMMETRY
SYMPTOTES
NTERVALS
AX MIN
NFLECTION
KETCH
4
New Information

• You know about vertical asymptotes
• You know about horizontal asymptotes
• What about other asymptotes?

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Example
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Example D
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Example I
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Example A
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Example S
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Example A
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Example A
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Example I
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Example M
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Example I
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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 rising.
Curve is falling.
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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Example
Graph
We can use a chart to organize our thoughts.
First derivative test
negative
positive
positive
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Example
Graph
First derivative test
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Example
Graph
NOTE On the AP Exam, it is not sufficient to
simply draw the chart and write the answer. You
must give a written explanation!
First derivative test
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Example
Graph
Or you could use the second derivative test
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Example
Graph
We then look for inflection points by setting the
second derivative equal to zero.
negative
positive
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Make a summary table
p
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Homework for Section 3.6

• 1-16, 31-38, 51-58
• Quiz Wednesday on Related Rates 2 Problems from
  Packet Answers Online
• Quiz Friday on MVT