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Calculus Notes 4.3: How Derivatives Affect the Shape of a Graph

Calculus Notes 4.3: How Derivatives Affect the Shape of a Graph 4.4: Limits at infinity; Horizontal Asymptotes. 4.5: Summary of Curve Sketching 4.6: Graphing with Calculus and Calculators. 4.5: Summary of Curve Sketching & 4.6: Graphing w/Calculus and Calculators.

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Calculus Notes 4.3: How Derivatives Affect the Shape of a Graph

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  1. Calculus Notes 4.3: How Derivatives Affect the Shape of a Graph 4.4: Limits at infinity; Horizontal Asymptotes. 4.5: Summary of Curve Sketching 4.6: Graphing with Calculus and Calculators 4.5: Summary of Curve Sketching & 4.6: Graphing w/Calculus and Calculators • Guidelines for Sketching a Curve: • Domain: what are you allowed to plug in for x • Intercepts: y intercept, plug in 0 for x; x intercept, plug in 0 for y • Symmetry: even, odd, periodic? • Asymptotes: Vertical: what makes denominator 0 (section 2.2 limit stuff); Horizontal: 4.4 material • Intervals of Increase or Decrease: Increase/Decrease Test from 4.3 • Local Maximum and Minimum values: find critical numbers, then max when f “ (c) < 0; min when f “ (c) > 0 as long as f “ (c) ≠ 0 • Concavity and points of Inflection: CU f “ (x) > 0; CD f “ (x) < 0; Points of Inflection when change concavity. • Sketch the curve.

  2. 4.5: Summary of Curve Sketching & 4.6: Graphing w/Calculus and Calculators Example 1: Graph the following, indicating all vertical and horizontal asymptotes, as well as slant asymptotes where applicable. • Domain: • Intercepts: • Symmetry: • Asymptotes: • Intervals of Increase or Decrease: none

  3. 4.5: Summary of Curve Sketching & 4.6: Graphing w/Calculus and Calculators Example 1: Graph the following, indicating all vertical and horizontal asymptotes, as well as slant asymptotes where applicable. • Domain: • Intercepts: • Symmetry: • Asymptotes: • Intervals of Increase or Decrease: • Local Maximum and Minimum values: • Concavity and points of Inflection: • Sketch the curve. none No inflection point.

  4. 4.5: Summary of Curve Sketching & 4.6: Graphing w/Calculus and Calculators Example 1: Graph the following, indicating all vertical and horizontal asymptotes, as well as slant asymptotes where applicable. PS 4.5 pg.270 #3, 6, 37, 42, 56 (5) PS 4.6 pg.277 #8, 9, 10, 13, 25 (5)

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