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3 Ltuts.),)wher F.,and v are differentiable. Suppose also that (-2-)1 (-2-3)--101, u (-2-3)-4, x (-2-3)--5 F (L-7)-3, F(-2-3)
consider the critical points (플,0)-@i), and (z-1) of a function f(xy) whose doman is restricted to p: {(х. У )I-1 s x s 4} an
3 Ltuts.),)wher F.,and v are differentiable. Suppose also that (-2-)1 (-2-3)--101, u (-2-3)-4, x (-2-3)--5 F (L-7)-3, F(-2-3)-3, F(I.-7)-2, and F.(-2-3)-0. Find W (-2-3 Circle your answer below o w(-2-3)-2 (e) W(-2-3)-12 ( W(-2-3)-14 (g) W(-2-3)-35 (h) W (-2,-3)-199 W(-2,-3)-202 M x2 + xy + y2 + 3y the local maximum and minimum values of the function f(x,y) 4. Find . Circle your answer below. (a) Relative minimum f(1.-2)--3, and no relative maximum. (b) No relative minimum, and relative maximum (1,-2)--3. (e) Relative minimum (l-2)--2, and relative maximum (1.-2)-1. (d) Relative minimum(l-2)--1, and relative maximum f(l.-2)-2. (e) Relative minimum f (1.-2)-3, and no relative maximum. () Relative minimum(l-2)--4, and local maximum f(1.-2)-1. g) No relative minimum and relative maximum. Relative minimum (l,-2)--2, and relative maximum f(l-2)-2
consider the critical points (플,0)-@i), and (z-1) of a function f(xy) whose doman is restricted to p: {(х. У )I-1 s x s 4} and whose partial derivatives are x,)-2ysin(x) and f,(x.y)-2y-2cos(x). What does the Second Derivatives Test tell us about the behavior of (x. y) near the critical points? Circle your answer below. (a) Relative maximum at both (0.1), and (n-l). relative minimum at . (b) Test fails at 0),relative maximum at (0.1). and relative minimum at ( ). (c) Test fails at ,0). relative maximum at (z-1), and relative minimum at (0 1) (a) Saddle point at relative minimum at (0.), and relative minimum at (z.-). (e) Saddle point at 1 쯔이, relative minimum at (r, i), and relative minimum at (0,1). (0 Saddle point at (r, -1), relative minumat o, and relative minimum at (0,1). (g) Test fails at (z-1), relative maximum at (0, 1), and relative minimum at I 쯔,0 (h) Test fails at all three critical points.
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U8ing Chain Rua 8,t) --2, -3) and C,u)(, -7) No w opton d and F Pind wR-2-3)? 8 w (-2,-3) - Fu Cl,-7) u,(-2,-3)) Vs (-2,-3) 2AC-B70 and A70 then FX,y) has cal id C2 y) Le(2) ()3 and xx 7 o and no Local mau mm ophon -Relative C-2)3 and Crítica, (중,o)a)(0,1) minimum relative f(x,y) (X,-1) hal → 3 At ak (π,-1) minimum relative hal f(x,y) 극 o ption e

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