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Unformatted text preview: Lecture 19 1 Lecture 19: (Sec. 4.1, part II) Relative Extrema ex. A Rational Function and Increasing, Decreasing Intervals Find all critical points for the function f ( x ) = 4 x + 1 x . Find the intervals on which f is increasing and decreasing. Lecture 19 2 Sketch the graph of y = 4 x + 1 x . Lecture 19 3 Relative Extrema and the First Derivative Test Def. Let y = f ( x ) and let c be in the domain of f . Then 1) f ( c ) is a relative maximum of f if there is an open interval ( a, b ) containing c so that for all x in the interval ( a, b ). 2) f ( c ) is a relative minimum of f if there is an interval ( a, b ) containing c so that for all x in the interval. NOTE: Lecture 19 4 Where do relative extrema occur for a con tinuous function? We note the following: If f has a relative extreme value at x = c , then That is, c is a critical point of f . Lecture 19 5 The First Derivative Test for Finding Rel ative Extrema Suppose that f is continuous on an interval contain ing a single critical point...
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This note was uploaded on 07/18/2011 for the course MAC 2233 taught by Professor Smith during the Spring '08 term at University of Florida.
 Spring '08
 Smith
 Calculus, Critical Point

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