lecture22

lecture22 - Lecture 22 1 Lecture 22(Sec 4.3 The Graph of a...

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Lecture 22 1 Lecture 22: (Sec. 4.3) The Graph of a Function Derivatives and the Shape of a Graph Sign of f Properties of the graph Shape and f 0 f of the graph f f 0 ( x ) > 0 f is f 00 ( x ) > 0 f is concave f 0 ( x ) > 0 f is f 00 ( x ) < 0 f is concave f 0 ( x ) < 0 f is f 00 ( x ) > 0 f is concave f 0 ( x ) < 0 f is f 00 ( x ) < 0 f is concave (Chart p. 273)

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Lecture 22 2 To sketch the graph of y = f ( x ) Look at the following: 1) y = f ( x ) a) domain b) range–if it can be determined easily c) vertical asymptote(s): one-sided limits d) horizontal asymptote(s): does the graph cross any horizontal asymptote? e) x and y intercepts 2) y = f 0 ( x ) a) critical points b) horizontal tangents, vertical tangents and cusps c) intervals where f is increasing/decreasing d) relative extrema 3) y = f 00 ( x ) a) concavity of the graph of f b) inﬂection points
Lecture 22 3 ex. Sketch the graph of f ( x ) = 3 x 5 - 5 x 3 .

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4 r 5 3 1 . 3, - 1 2 ≈ - 0 . 7, 1 2 0 . 7, f - 1 2 ! 1
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lecture22 - Lecture 22 1 Lecture 22(Sec 4.3 The Graph of a...

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