math117_assignment08 - - -_._. "- _ . "'. Math...

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------_ ...... _ _. ""- .. "'.- Math 117 Assignment 8 Fall 2008 Due November 13th or 14th 1. To locate the absolute extrema of a function on a closed interval, it is not necessary to classify local extrema. Instead, all we need to do is find all of the local extrema and compare the corresponding values of the function, along with its values at the endpoints of the interval. The largest and smallest of these values must be the absolute maximum and minimum. This is known as the "Closed Interval Method" for locating absolute extrema. a) Find the absolute maximum and minimum values of the function f(x) = X4 - 3x 3 + 3x 2 - x on the interval [0,2]. b) Locate any inflection points and sketch f on [0,2]. 2. An open water conduit is to be cut in the shape of an isosceles trapezium and lined with material which is available in a standard width of 1 metre as shown in the figure. b b To achieve maximum potential capacity, the designer has to maximize the area of cross-section A(b). Show that A(b) = [(1 + b)3(1-
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math117_assignment08 - - -_._. "- _ . "'. Math...

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