Day-10 - Example 3: Find the relative extrema of the...

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
Math 1314 Day 10 Let 2 ) ( ) , ( xy yy xx f f f y x D - = . You will compute ) , ( b a D for each critical point ). , ( b a Here’s the second derivative test for functions of two variables : If D(a, b) > 0 and 0 ) , ( < b a f xx , then f has a relative maximum at ( a, b ). If D(a, b) > 0 and 0 ) , ( b a f xx , then f has a relative minimum at ( a, b ). If D(a, b) < 0, then f has neither a relative maximum nor a relative minimum at ( a, b ) (i.e., it has a saddle point, which is neither a max nor a min). If D(a, b) = 0, then this test is inconclusive.
Background image of page 1

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

View Full DocumentRight Arrow Icon
Background image of page 2
Background image of page 3

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

View Full DocumentRight Arrow Icon
Background image of page 4
Background image of page 5
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Example 3: Find the relative extrema of the function . 2 3 6 6 ) , ( 2 3-+ +-+ = y x xy y x y x f Example 4 : Find the relative extrema of the function 3 2 ( , ) 2 5 f x y x xy y = -+--. Example 5 : An open box with a volume of 48 cubic inches is to be constructed. The box is to have a partition that is parallel to a side of the box, and the amount of material used is to be minimal. What should be the dimensions of the box?...
View Full Document

This note was uploaded on 02/21/2012 for the course MATH 1314 taught by Professor Marks during the Fall '08 term at University of Houston.

Page1 / 5

Day-10 - Example 3: Find the relative extrema of the...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online