mid2samp2soln - Math 1A, Spring 2008, Wilkening Another...

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Math 1A, Spring 2008, Wilkening Another Sample Midterm 2 1. (1 point) write your name, section number, and GSI’s name on your exam and write your name on your sheet of notes. 2. (3 points) Suppose f is twice differentiable on the interval [0 , 4] and satisfies f 0 (0) = 1 f 00 (0) = - 1 f 0 (1) = 0 f 00 (1) = - 2 f 0 (2) = 0 f 00 (2) = 0 f 0 (3) = - 1 f 00 (3) = 1 f 0 (4) = 0 f 00 (4) = 1 At the endpoints x = 0 and x = 4, these are one-sided derivatives. Fill in the following table with YES, NO, or CBT (cannot be determined). c = 0 1 2 3 4 f has a local max at c No Yes, f 00 (1) < 0 CBT No, f 0 (3) 6 = 0 No f has a local min at c Yes, f 0 (0) > 0 No CBT No, f 0 (3) 6 = 0 Yes, f 00 (4) > 0 3. (5 points) Let f ( x ) = x x . Compute f 0 (2), f 0 (4) and ( f f ) 0 (2). Note that 4 4 = 256. y = f ( x ) = x x = ln( y ) = ln( x x ) = ln( y ) = x ln( x ) 1 y dy dx = ln( x ) + x x = 1 y dy dx = ln( x ) + 1 = dy dx = y (ln( x ) + 1) = f 0 ( x ) = x x (ln( x ) + 1) ( f f ) 0 = ( f ( f ( x ))) 0 = f 0 ( f ( x
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This note was uploaded on 09/24/2009 for the course MATH 1A taught by Professor Wilkening during the Spring '08 term at University of California, Berkeley.

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mid2samp2soln - Math 1A, Spring 2008, Wilkening Another...

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