{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

508F06Ex2s(1)

# 508F06Ex2s(1) - Signature Printed Name Exam 2 Math 508...

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

Signature Printed Name Math 508 Exam 2 Jerry L. Kazdan December 8, 2006 12:00 – 1:20 Directions This exam has two parts, Part A has 3 shorter problems (8 points each, so 24 points), Part B has 5 traditional problems (15 points each, so 75 points). Closed book, no calculators – but you may use one 3 00 × 5 00 card with notes. Part A: Short Problems (3 problems, 8 points each). A–1. A continuous function f : R R has the property that Z x 0 f ( t ) dt = cos( x ) e - x + C, where C is some constant. Find both f ( x ) and the constant C . A–2. A function h : R R with two continuous derivatives has the property that h (0) = 2, h (1) = 0, and h(3)=1. Prove there is at least one point c in the interval 0 < x < 3 where h 00 ( c ) > 0 by finding some explicit m > 0 (such as m = 2 / 3) with h 00 ( c ) m . A–3. Say a smooth function u ( x ) satisfies u 00 - c ( x ) u = 0 for 0 x 1 (here c ( x ) is some given contunuous function). If c ( x ) > 0 everywhere, show that there is no point where u ( x ) is both positive and has a local maximum.

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.

{[ snackBarMessage ]}