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Unformatted text preview: Lecture 21 1 Lecture 21, Part I: (Sec. 4.2, part II) ex. Find the intervals on which f ( x ) = 3 x 5 5 x 3 is concave up and down, and each xvalue at which the graph of f has an inflection point. Lecture 21 2 The Second Derivative Test Extrema and the Second Derivative Suppose continuous function f is differentiable and has a relative extreme value at x = c . Relative Minimum Relative Maximum Lecture 21 3 The Second Derivative Test for Relative Extrema: For a function f , 1) Find f ( x ) to locate the critical points of f . 2) For each critical point c so that f ( c ) = 0, find f 00 ( c ). We can conclude: 1) If f 00 ( c ) > 0, 2) If f 00 ( c ) < 0, 3) If f 00 ( c ) = 0, Lecture 21 4 ex. Use the Second Derivative Test to find the relative extreme values of f ( x ) = 3 x 5 5 x 3 . Lecture 21 5 Note the following about the Second Derivative Test: 1) 2) 3) Lecture 21 6 Lecture 21, part II(Sec. 4.3, part I) Asymptotes Vertical Asymptotes ex. Let f ( x ) = 1 x 2 Def. The line x = a is a vertical asymptote(VA) of the graph of a function f if Lecture 21 7 ex. Given f ( x ) = 2 x x + 3 ....
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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, Derivative

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