Math241_Fall08_9AM_Exam3

# Math241_Fall08_9AM_Exam3 - Math 241 – Exam 3 – 9AM V1...

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

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.

Unformatted text preview: Math 241 – Exam 3 – 9AM V1 Name: November 16, 2008 Section Registered In: 55 points possible 1. Let f : R n → R . (a) (3pts) State the formula for the second-order Taylor polynomial of f at the point ~a in R n . (b) (2pts) In order for this expansion to be valid, we require that f be C k . Briefly explain what the value of k must be. (c) (3pts) How did we use the second-order Taylor polynomial to derive the second-derivative test for local extrema? Briefly explain. 2. (7pts) Let f ( x,y,z ) = x 3 + x 2 y- yz 2 + 2 z 3 . Find the second-order Taylor polynomial of f at the point (1 , , 1). (You do not need to simplify your answer.) 3. Let f ( x,y,z ) = x 3 + xy 2 + x 2 + y 2 + 3 z 2 . (a) (3pts) Show that the point- 2 3 , , ¶ is a critical point of f . (b) (2pts) If H f (- 2 3 , , ) = - 2 0 0 2 3 0 6 , classify the critical point. 4. (8pts) Find the maximum and minimum values of f ( x,y ) = y 2- x + 200 subject to the constraint x 2 + y 2 = 1.= 1....
View Full Document

{[ snackBarMessage ]}

### Page1 / 4

Math241_Fall08_9AM_Exam3 - Math 241 – Exam 3 – 9AM V1...

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

View Full Document
Ask a homework question - tutors are online