1001_4.1_Lab_16

1001_4.1_Lab_16 - " " f ( x )...

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CALCULUS 1 LAB 16 NAME: ___________________PARTNER: _________________ 4.1 Analysis of Functions I GSA:______________________Lab Time: ____________ Basic Guidelines: Critical Points; Intervals where f ( x ) is Increasing, Decreasing, Concave Up or Concave Down. * A function f ( x ) has a critical point c if f ( c ) exists and " f ( c ) = 0 (a Stationary Point) or " f ( c ) does not exist. * f ( x ) is increasing on an open interval where " f ( x ) > 0 or decreasing on an open interval where " f ( x ) < 0 : Take the first derivative, find the critical points and then make a sign analysis. * f ( x ) is concave up on an open interval where " " f ( x ) > 0 or concave down on an open interval where " " f ( x ) < 0 . Take the second derivative and make a sign analysis. * To find the x -coordinates of all inflection points: Look for a change of concavity where
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Unformatted text preview: &quot; &quot; f ( x ) changes sign. Note: The function will be increasing or decreasing on a closed interval if it is continuous on that interval. 1. Let f ( x ) = x 3 &quot; 12 x . a) Find the critical points of f ( x ) . b) Make a sign analysis of &quot; f ( x ) or sign line or table. c) Find the closed intervals (if it is possible to include the critical point/points) on which f ( x ) is increasing or decreasing. d) Make a sign analysis of &quot; &quot; f ( x ) or sign line or table. e) Find the open intervals on which f ( x ) is concave up or concave down. f) Find the x-coordinate of any inflection points and make a sketch with all critical points and inflection points labeled. 2. Repeat for f ( x ) = e &quot; 2 x 2 ....
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