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9. Locate all relative maxima, relative minima, and saddle points of the fol- lowing function f(x, y) = x² + y² - x²y. The second partial derivative test is: D(x, y) = fez(x, y) fyy (x, y) - (fxy(x, y))². •If D(xo, yo) > 0, and - if fax (xo, yo) > 0, then f has a relative (local) minimal at (xo, yo); then f has a relative (local) maximal at (xo, yo); if frx (xo, yo) <0, If D(xo, yo) <0, then (xo, yo) is a saddle point; • If D(xo, yo) = 0, no conclusion about (xo, yo).

9. Locate all relative maxima, relative minima, and saddle points of the fol- lowing function f(x, y) = x² + y² - x²y. The second partial derivative test is: D(x, y) = fez(x, y) fyy (x, y) - (fxy(x, y))². •If D(xo, yo) > 0, and - if fax (xo, yo) > 0, then f has a relative (local) minimal at (xo, yo); then f has a relative (local) maximal at (xo, yo); if frx (xo, yo) <0, If D(xo, yo) <0, then (xo, yo) is a saddle point; • If D(xo, yo) = 0, no conclusion about (xo, yo).

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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9. lowing function Locate all relative maxima, relative minima, and saddle points of the fol- ● The second partial derivative test is: • 1 f(0)-²+²-2². 1 If D(ro, yo) > 0, and = D(x, y) = fxx (x, y) fyy (x, y) — (fxy(x, y))². - - if fxr (To, yo) > 0, then f has a relative (local) minimal at (xo, yo); - if fxx (xo, yo) <0, then f has a relative (local) maximal at (xo, yo); If D(xo, yo) <0, then (xo, yo) is a saddle point; If D(xo, yo) = 0, no conclusion about (xo, yo).
Transcribed Image Text:9. lowing function Locate all relative maxima, relative minima, and saddle points of the fol- ● The second partial derivative test is: • 1 f(0)-²+²-2². 1 If D(ro, yo) > 0, and = D(x, y) = fxx (x, y) fyy (x, y) — (fxy(x, y))². - - if fxr (To, yo) > 0, then f has a relative (local) minimal at (xo, yo); - if fxx (xo, yo) <0, then f has a relative (local) maximal at (xo, yo); If D(xo, yo) <0, then (xo, yo) is a saddle point; If D(xo, yo) = 0, no conclusion about (xo, yo).
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