{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

3.4 pt2 - 210 3 Higher Derivatives and Extrema 11 12 13 14...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 210 3. Higher Derivatives and Extrema 11. 12. 13. 14. 15. 16. 17. 18. s 19. 20. 21. 22. 25. f(1,y) = a32+y2 +539 —-4y+ l3 f(a:,y} =:t:2+y2 +3a:—2y+ 1 ﬂay) e29 —y2+:cy—7 flay) = 2:2 +312 +331: + 10 f{:c,y) 22:2 -— 3\$y+5ath 2y+ﬁy2+8 flay) = x2 + ryz +31“ ﬂaw) = Elm—”2 to. y) = (m2 + wee-v“ ﬂay) = log(2 + sinacy) [Consider only the critical point (0,0}.] fix, y) = sin (a:2 + 3,12) [Consider only the critical point (0, 0).] Let ﬂat-,y) = 3:2 + y? + key. If you imagine the graph changing as it increases. at what values of It does the shape of the graph change quali- tatively? Find the local maxima and minima for z = (5:2 + 3y2)e1"2_y2. (See Figure 2.1.23.) An examination of the function f(:r:,y) = (y — 3x2](y — 1:2) will give a: idea of the difficulty of ﬁnding conditions that guarantee that a criticai point is a relative extremum when the second derivative test fails. Show that (a) the origin is a critical point of f; (b) f has a relative minimum at (0, D) on every straight line through [0. O r; that is, if 9(3) = (at,bt), then f o g : R —+ R has a relative minimum a: O, for every choice of o. and b; (c) the origin is not a relative minimum of f. 24. Let n be an integer greater than 2 and set f(a:,y) = arr" + 0y“, where as 79 0. Determine the nature of the critical points of f. ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online