Lecture 5.4 - Chapter 5 Graphing and Optimization Section 4...

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Chapter 5 Graphing and Optimization Section 4 Curve Sketching Techniques
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2 Barnett/Ziegler/Byleen Business Calculus 12e Objectives for Section 5.4 Curve Sketching Techniques The student will modify his/her graphing strategy by including information about asymptotes. The student will be able to solve problems involving modeling average cost.
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3 Barnett/Ziegler/Byleen Business Calculus 12e Modifying the Graphing Strategy When we summarized the graphing strategy in a previous section, we omitted one very important topic: asymptotes . Review of Asymptotes is needed.
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4 Partition Numbers and Critical Values A partition number for the sign chart is a place where the derivative could change sign. This can only happen: - at vertical asymptotes: where f itself is not defined - at critical values - where f is not defined - where f is zero You must check the sign of the critical values on both sides of the critical points to see if the derivative changes signs.
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5 Barnett/Ziegler/Byleen Business Calculus 12e 0 0 0 1 1 lim 1 lim 1 lim Does not exist 1 lim 0 1 lim 0 x x x x x y x x x x x x + →∞ →−∞ = = ∞ = −∞ = = Asymptotes and Limits Involving Powers of x 2 2 0 2 0 2 0 2 2 1 1 lim 1
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Lecture 5.4 - Chapter 5 Graphing and Optimization Section 4...

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