Unformatted text preview: f is concave down on I . The Concavity Test p.291 a) If ( ) f x ′′ > for all x in I , then the graph of f is concave up on I . b) If ( ) f x ′′ < for all x in I , then the graph of f is concave down on I . Def. p.291 A point P on a curve ( ) y f x = is an inflection point if f is continuous there and the curve changes concavity at P . The Second Derivative Test (for Local Extrema) p.292 Suppose f ′′ is continuous near c . a) If ( ) f c ′ = and ( ) f c ′′ > , then f has a local minimum at c . b) If ( ) f c ′ = and ( ) f c ′′ < , then f has a local maximum at c . Guidelines for Curve Sketching (pp.308309) A. Domain B. Intercepts C. Symmetry D. Asymptotes E. Intervals of Increase/Decrease F. Local Maximum or Minimum Values; Terrace Points G. Concavity and Inflection Points...
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 Spring '11
 Teague
 Calculus, Critical Point, Derivative, Mathematical analysis, local maximum

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