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140Bquiz6csols

140Bquiz6csols - 1 MATH 140B QUIZ#6 Solutions Due Mon Oct 8...

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Unformatted text preview: 1 MATH 140B QUIZ#6 Solutions Due: Mon Oct 8, 2007 1. i) True . ( f Β· g ) β² (0) = f (0) g β² (0) + f β² (0) g (0) = (3)(0) + (2)( β 3) = β 6 . ii) False . ( f/g ) β² (4) = g (4) f β² (4) β f (4) g β² (4) g (4) 2 = (2)(5) β (1)( β 2) 2 2 = 12 4 = 3 . iii) False . ( f β¦ g ) β² ( β 1) = f β² ( g ( β 1)) Β· g β² ( β 1) = f β² (4) Β· ( β 3) = 5 Β· ( β 3) = β 15 . Therefore, A) is the answer. 2. i) True . By definition of local maximum and local minimum. ii) True . At all points x in the interval (2 , 5) , f β² ( x ) = 0 (horizontal tangent), so these points are all critical points. That certainly makes infinitely many. iii) True . Local minima occur at all points x in the interval (2 , 5) . The statement makes no claim about the endpoints x = 2 and x = 5 , so we donβt need to address them. Therefore, E) is the answer. 3. i) True . Using the product rule, f β² ( x ) = x 2 Β· 1 2 (1 β x 2 ) β 1 / 2 ( β 2 x ) + 2 x (1 β x 2 ) 1 / 2 = x (1 β x 2 )...
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