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Unformatted text preview: Math 9A Quiz 6 Tuesday, May 22 2007 Name: 1. Find the absolute maximum and minimum values of the function f ( x ) = 1 x on the interval [ 2 , 1], and identify values where they occurr. Solution: First we must find the critical points of f ( x ). We have f ( x ) = 1 /x 2 . There are no points c such that f ( c ) = 0 (this derivative is never =0), but there is one point c such that f ( c ) is undefined: c = 0. Therefore c = 0 is a critical point. Next we evaluate f ( x ) at all of the critical points we’ve find which lie in the interval [ 2 , 1] and at the endpoints of the interval. Since the function’s only critical point, c = 0, does not lie within the given interval we do not need to consider it at all here. Evaluating f ( x ) at the endpoints gives us f ( 2) = 1 2 ; f ( 1) = 1 . Therefore, on the interval [ 2 , 1], the absolute minimum of f ( x ) is 1 / 2, occurring at x = 2, and the absolute maximum is 1, occurring at x = 1....
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This test prep was uploaded on 04/16/2008 for the course MATH 9A taught by Professor Apoorva during the Winter '07 term at UC Riverside.
 Winter '07
 APOORVA
 Critical Point

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