mid2samp2soln

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online