{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Day-10-filled

# Day-10-filled - Example 3 Find the relative extrema of the...

This preview shows pages 1–6. Sign up to view the full content.

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.

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

View Full Document

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

View Full Document

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: 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

{[ snackBarMessage ]}