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

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Unformatted text preview: 1 MATH 140B QUIZ#6 Solutions Due: Mon Oct 8, 2007 1. i) True . ( f g ) (0) = f (0) g (0) + f (0) g (0) = (3)(0) + (2)( 3) = 6 . ii) False . ( f/g ) (4) = g (4) f (4) f (4) g (4) g (4) 2 = (2)(5) (1)( 2) 2 2 = 12 4 = 3 . iii) False . ( f g ) ( 1) = f ( g ( 1)) g ( 1) = f (4) ( 3) = 5 ( 3) = 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 ( 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 dont need to address them. Therefore, E) is the answer. 3. i) True . Using the product rule, f ( x ) = x 2 1 2 (1 x 2 ) 1 / 2 ( 2 x ) + 2 x (1 x 2 ) 1 / 2 = x (1 x 2 )...
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This note was uploaded on 03/30/2008 for the course MATH 140B taught by Professor Fabbri,marc during the Fall '07 term at Pennsylvania State University, University Park.

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