{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# pset8 - 18.06 Problem Set 8 Due Wednesday 23 April 2008 at...

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

18.06 Problem Set 8 Due Wednesday, 23 April 2008 at 4 pm in 2-106. Problem 1: Do problem 3 in section 6.5 (pg. 339) in the book. Problem 2: Do problem 6 in section 6.5 (pg. 339). Problem 3: For what numbers c and d are the matrices A and B positive definite? Test the 3 determinants: A = c 2 3 2 c 4 3 4 1 B = 1 2 1 2 d 3 1 3 1 Problem 4: Do problem 15 in section 6.5 (pg. 340). Problem 5: Do problem 28 in section 6.5 (pg. 342). Problem 6: a) Let f 1 ( x, y ) = 1 4 x 4 + x 2 y + y 2 . Find the second derivative matrix A 1 = 2 f/∂x 2 2 f/∂x∂y 2 f/∂y∂x 2 f/∂y 2 A 1 is not positive definite everywhere - find the conditions on x and y for it to be positive definite. (Interesting question: check what happens when both partial derivatives vanish, that is, when ∂f/∂x = ∂f/∂y = 0. Is f still positive definite? It turns out that f 1 does attain a minimal value, but not along isolated points. Find the points where it hits a global minimum. This part is not required.) b) Let f 2 ( x, y ) = x 3 + xy - x . Find the second derivative matrix

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 ]}

### Page1 / 3

pset8 - 18.06 Problem Set 8 Due Wednesday 23 April 2008 at...

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

View Full Document
Ask a homework question - tutors are online