Exam2_2 4 - 1. B only 2. A only correct 3. Both of them 4....

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Taylor, Douglas – Exam 2 – Due: Oct 31 2007, 1:00 am – Inst: JEGilbert 4 1. none of these 2. abs. min. value = 2 3. abs. min. value = 4 correct 4. abs. min. value = 3 5. abs. min. value = 5 Explanation: The absolute minimum value of f on [0 , 3] occurs either at an endpoint of [0 , 3] or at a critical point of f in (0 , 3). Now f 0 ( x ) = x 2 - 10 x + 16 = ( x - 2)( x - 8) , so the critical points of f occur at x = 2 , 8. But only x = 2 lies in (0 , 3). On the other hand, f (0) = 4 , f (2) = 56 3 , f (3) = 16 . Consequently, abs. min. value = 4 . keywords: absolute minimum, polynomial 009 (part 1 of 1) 10 points Let f be the function deFned by f ( x ) = 3 + 2 x 1 / 3 . Consider the following properties: A. concave up on ( -∞ , 0); B. has horizontal tangent at x = 0 . Which does f have?
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Unformatted text preview: 1. B only 2. A only correct 3. Both of them 4. Neither of them Explanation: The graph of f is 2 4-2-4 2 4 6 On the other hand, after dierentiation, f ( x ) = 2 3 x 2 / 3 , f 00 ( x ) =-4 9 x 5 / 3 . Consequently, A. has: ( f 00 ( x ) > , x < 0); B. not have: (see graph). keywords: horizontal tangent, concavity, True/alse, graph 010 (part 1 of 1) 10 points Which one of the following properties does f ( x ) = x-4 x 2 + 20 have? 1. local min at x = 10 2. local min at x =-10 3. local max at x = 10 correct 4. local max at x =-10 5. local max at x = 2 6. local min at x = 2 Explanation:...
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This note was uploaded on 02/14/2012 for the course MATH 408 K taught by Professor Clark,c.w./hoy,r.r during the Spring '08 term at University of Texas at Austin.

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