MATH 1920 Lecture Notes - Lecture 17: Maxima And Minima, Lagrange Multiplier, Minimax

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4 Oct 2017

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Method: to find the maximum or minimum of f(x, y) on d. Find the critical points of f that are inside d (not on the boundary) and evaluate f at each point. Locate and evaluate extreme values of f on the boundary of d. The maximum/minimum of d is on this list. Example: ! (#, %) = #( 2#% + % d = [0, 3] (cid:1) [0, 2] Critical point (a, b): ,! (/, 0) = 1. Only critical point: (1, 1) f(1, 1) = 1. Step 2: split the boundary of d into 4 lines. L1: y = 0 for x [0, 3] (#, 0) = #( for # [0,3] L2: x = 0 for y [0,2] (0, %) = 2% L3: y = 2 for x [0,3] (#, 2) = #( 4# + 4. Maximum is either: (0,2) = 4 or (3,2) = 1.

Related Questions

A. Find the critical points.

B. Use the second derivative test to

classify each critical point.

f (x, y) = âx^3 + 9xy â y^3

A. (1,1)and(0,0)

B. (3,3)and(0,0)

C. (1, 1) only
D. (-3, -3) and (0, 0)

E. (-3, -3) only

F. not listed

B. Which are true?

A. The critical points generate one relative maximum and one relative minimum. B. The critical points generate one relative maximum and one saddle point.

C. The critical points generate one relative minimum.
D. The critical points generate one relative minimum and one saddle point.

E. The second derivative test was inconclusive about all critical points.
F. None of the statements is true.

A. Find the critical points.

B. Use the second derivative test to

classify each critical point.

C. Find the relative extrema of the

function.

f(x,y)=2x^2âxy+y^2â3xây+3

A. (1, -2)
B. (2, -1)
C. (1, -1)
D. (1, 1)
E. Not listed

A. relative minimum at the critical point

B. relative maximum at the critical point

C. saddle point at the critical point
D. no result at the critical point

E. not listed

A. relative minimum value is 0
B. relative maximum value is 0
C. relative minimum value is 1
D. relative maximum value is 1
E. there are no relative extrema or the test failed at the critical point F. not listed.

MATH 1920 Lecture Notes - Lecture 17: Maxima And Minima, Lagrange Multiplier, Minimax

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