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Assignment2(0211)

Assignment2(0211) - A2/MATH0211/2009-10 THE UNIVERSITY OF...

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A2/MATH0211/2009-10 THE UNIVERSITY OF HONG KONG DEPARTMENT OF MATHEMATICS MATH0211 Basic Applicable Mathematics Assignment 2 Due date : Sep 30, 2009 before 17:00. Remember to write down your Name , Uni. number and Tutorial Group number . You are welcome to see the instructor or demonstrator if you have any difficulties. See “Course information” at http://147.8.101.93/MATH0211 for availabilities. Please drop your work in the assignment box marked MATH0211 on the 4th floor of Run Run Shaw Building. No late work will be accepted. 1. Let f ( x ) = | x - 1 | + | x - 2 | . (a) Write f ( x ) as a case-defined function. (b) Sketch the graph of f ( x ) . (c) Find the range of f ( x ) by projecting its graph onto the y -axis. (d) Use the horizontal line test to check if f ( x ) is injective on [1 , 2] . 2. Let f ( x ) = ax 2 + bx + c be a quadratic function. (a) Show that f ( x ) can also be written as f ( x ) = a x + b 2 a 2 - b 2 - 4 ac 4 a . (b) If a is negative, use (a) to show that the function f has a maximum value when x = - b/ 2 a .
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