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# L26 - L26 Curve Sketching Use f(x for nding Domain...

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L26 – Curve Sketching Use f ( x ) for finding: Domain Intercepts Symmetry Asymptotes Use f 0 ( x ) for finding: Critical Numbers Increasing/Decreasing Local Extrema Use f 00 ( x ) for finding: Concavity Points of Inflection 1

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f ( x ) = x 2 + 1 1 - x 2 f 0 ( x ) = 4 x (1 - x 2 ) 2 f 00 ( x ) = 4 + 12 x 2 (1 - x 2 ) 3 2
f ( x ) = ( x 2 - 1) 2 3 f 0 ( x ) = 4 x 3( x 2 - 1) 1 3 f 00 ( x ) = 4( x 2 - 3) 9( x 2 - 1) 4 3 f ( ± 3) 1 . 6 3

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f ( x ) = x 1 3 ( x - 4) f 0 ( x ) = 4 x - 4 3 x 2 3 f 00 ( x ) = 4 x + 8 9 x 5 3 4
f ( x ) = x ln( x ) lim x 0 f ( x ) = 0 f 0 ( x ) = 1 + ln( x ) f 00 ( x ) = 1 x 5

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f ( x ) = e - 1 x f 0 ( x ) = e - 1 x x 2 f 00 ( x

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