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2. For each function, find all critical points and use the Hessian to determine whether they...

2. For each function, find all critical points and use the Hessian to determine whether they are local maxima, minima, or sad

2. For each function, find all critical points and use the Hessian to determine whether they are local maxima, minima, or saddle points. (a) f(x,y,z) = x — 2 sin x – 3yz (b) g(x, y, z) = cosh x + 4yz – 2y2 – 24 (c) u(x, y, z) = (x – z)4 – x2 + y2 + 6x2 – 22
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27 So - 3 Zz 0 ) Zzo 3Y 2 2. a> f(x,y,z) 2 x - 2 Sinx - 3yZ For critical points, af, af, at zo of 1 - 2 cosx = 0 =) ces XzK cX b) g(x,y, 2) a coshx + 4y2-24²-29 +447 - 24 – ZA 29 sinha 2 2 32x20 2x 2x22 29 47 - 4y = = 0z) Zzay afy 244y -47% -0 => Y =c) u(x, y, z) 2 (x-7)9 _x²+7²+ 6x2 – z2 2x = 4(x-7)3 - 2x +67-0-02 2 2yzo 2z 4Z - 22 27 2) yao 2-4 (x-2)3 + 6x = 0 ;) (i) + (

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