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Calculus Review: Critical Numbers, Increasing/Decreasing Intervals, Extrema, Concavity, and Inflection Points

This review covers finding critical numbers, determining increasing/decreasing intervals, applying the First and Second Derivative Tests to identify extrema, analyzing concavity, and finding inflection points.

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Calculus Review: Critical Numbers, Increasing/Decreasing Intervals, Extrema, Concavity, and Inflection Points

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  1. QUIZ REVIEW SECTION 3.3/3.4 • There are 3 slides. Each slide will remain up for 12 minutes. • Be sure to read all directions. • You may use the graphing calculator as a guide and assistance but you must show all work! • We will be going over the review in 50 minutes

  2. (a) Find the critical numbers of f (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema: 1. f(x) = 2. f(x) = sin x [0, 2π]

  3. Determine the open intervals on which the graph is concave upward or concave downward: f(x) = 4. Find the points of inflections and discuss the concavity of the graph of the function: f (x) =

  4. 5. Find all relative extrema. Use the Second Derivative Test where applicable: • (a) Find the critical numbers of f (if any), (b) find the open interval(s) on which the function is increasing or decreasing, (c) apply the First Derivative Test to identify all relative extrema, (d) find the open interval(s) on which the function is concave up or concave down, (e) find the points of inflection (if any):   f(x) =

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