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Unformatted text preview: L26 – Curve Sketching Use f (x) for ﬁnding: Domain Intercepts Symmetry Asymptotes Use f (x) for ﬁnding: Critical Numbers Increasing/Decreasing Local Extrema Use f (x) for ﬁnding: Concavity Points of Inﬂection 1 f (x) = x2 + 1 1 − x2 4x (1 − x2 )2 4 + 12x2 (1 − x2 )3 f (x) = f (x) = 2 f (x) = (x2 − 1) 3 2 f (x) = 4x 3(x2 − 1)
1 3 f (x) = 4(x2 − 3) 9(x2 − 1) 3
4 √ f (± 3) ≈ 1.6 3 f (x) = x 3 (x − 4) 4x − 4 3x 3
2 1 f (x) = f (x) = 4x + 8 9x 3
5 4 f (x) = x ln(x) x →0 lim f (x) = 0 f (x) = 1 + ln(x) f (x) = 1 x 5 f (x) = e− x
1 1 1 e− x f (x) = 2 x e− x (1 − 2x) f (x) = x4 6 f (x) = 1 sin(2x) + sin(x) 2 f (x) = −2 sin(2x) − sin(x) 5π ) ≈ −1.3 3 f (x) = cos(2x) + cos(x) π ) ≈ 1.3 3 f( f( 7 f (x) = x (1 − x2 ) 2 1 (1 −
3 x2 ) 2 1 f (x) = f (x) = 3x (1 − x2 ) 2
5 8 ...
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 Fall '08
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 Calculus, Asymptotes

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