1007_Tut2_Sol

1007_Tut2_Sol - MATH 1007 A Tutorial#2 Solutions 1[3 marks...

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Unformatted text preview: MATH 1007 A Tutorial #2 Oct 13, 2006 Solutions 1. [3 marks] Find the absolute maximum and the absolute minimum of f ( x ) = x 3- 6 x 2 + 9 x + 2 on the interval [- 1 , 4]. Where does the absolute maximum occur? Where does the absolute minimum occur? Note: You must clearly demonstrate that you have checked all relevant values of f and give a sentence answer. Solution: f ( x ) = 3 x 2- 12 x + 9 = 3( x 2- 4 x + 3) = 3( x- 1)( x- 3) f ( x ) = 0 ⇐⇒ x = +1 or x = +3 (both are inside [-1,4]) f (- 1) =- 1- 6- 9 + 2 = 2- 16 =- 14 f (+1) = 1- 6 + 9 + 2 = 12- 6 = 6 f (+3) = 27- 54 + 27 + 2 = 2 f (+4) = 64- 96 + 36 + 2 = 102- 96 = 6 On the interval [- 1 , 4], the absolute maximum of f is +6 and occurs in 2 places: at x = +1 and at x = +4, and the absolute minimum is- 14 and occurs when x =- 1. Note: Students should NOT calculate f (0) or f (2). If they do (and include all of the above work as well), please give only 2 marks out of 3. 2. [1 mark] If f ( x ) = ( x- a )( x- b )( x- c ), show that...
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1007_Tut2_Sol - MATH 1007 A Tutorial#2 Solutions 1[3 marks...

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