1001_4.4_Lab_20

1001_4.4_Lab_20 - * If there is only one relative minimum...

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CALCULUS 1 LAB 20 NAME: ___________________PARTNER: _________________ 4.4 Finding Absolute Maxima and Minima GSA: ______________________Lab Time: ____________ Basic Guidelines: Absolute Extrema are functional values, y-values. On Closed Intervals [ a , b ] : Step 1: Find all the critical points. Step 2: Substitute each of the critical points and the end points into f(x) to find the values. * The smallest is the Absolute Minima and the largest is the Absolute Maxima . On Open Intervals ( a , b ) with one relative extrema: * If there is only one relative maximum on an open interval, then it is the absolute maximum.
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Unformatted text preview: * If there is only one relative minimum on an open interval, then it is the absolute minimum. Step 1: Find all the critical points. There should only be one on the given open interval. Step 2: Make a sign analysis of ) ( ' x f and use the FDT to find the absolute extreme value. Or, Step 3: Use the SDT to find the absolute extreme value. Find the Absolute Maxima and Absolute Minima. 1. f ( x ) = ( x " 1) 3 on [0, 3]. 2. f ( x ) = 3 " 4 x " 2 x 2 on ( "# , + # ) . 3. f ( x ) = x 3 " 6 x 2 + 7 on [-2, 2] and also on (2, 6)....
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