Which of the following is true if* f(x, y) = 2- 2xy + xy³ + 3y? frz (x, y) = 6x fyy (z, y) = 6+ 6xy fry (x, y) = -2+ 3y? j.(2,v) = 3z-2y+ y² f,(z,y) = -2z+6y + 3ry fry(z, y) = 6z

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Q: 2z + 5z + 14 If U(z) = evaluate u %3D Uz and (z – 1)

A: Solution :

Q: 1. Let f(x, y) = In(x - y) then at the point (4,1), fryis equal to: %3D -1/9 O 1/7 1/9

A: Thanks for the question :)And your upvote will be really appreciable ;)

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A: U→=exyax+sin(xy)ay+cos2(xz)az

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A: Vf(x,y) =[d/dx(f(x,y) ,d/dy(f(x,y)]

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A: Given problem is solved below.

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A: Note: There are many subparts in the question. So I will answer first subparts in the question.…

Q: Find curl F if F(x,y,z) = 16y5₂5i - 8x³₂8 j- 7xy4k. O curl F = (-28xy3 +64x³₂7)i + (7y4 + 80y5z4)j +…

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A: If fx,y,z =xcos2y-z....icompute dfdx and dfdz

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A: To evaluate

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A: We have to prove this

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A: Define D(x,y)=fxx(x,y)fyy(x,y)-[fxy(x,y)]2                                  =x2y2-22…

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A: It should by x/y, instead of x/z

Q: Suppose we know the following: z = f(x, y) where x = 2v-u, y=v² +2u, (-3,2)= 12, fy(-3,2)= -15,…

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Q: Minimize c = s + t + 2u subject to s + 4t + 2u ≥ 95 4s + t + 3u ≥ 95 s ≥ 0, t ≥ 0, u ≥ 0. c= (s, t,…

A: the given simplex problem is as follows  Minimize c=s+t+2u subject to…

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Q: If G (x, y, z) = curlF (x, y, z), where F (x, y, z) = (y – 2, z – x, x – y), then х, х — у), then ||…

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Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

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Q: If (2, 1) is a critical point of f and fzz(2,1)ƒyy(2, 1) < [ƒzy(2, 1)]², then ƒ has a saddle point…

A: Here, the given statement is: If (2,1) is a critical point of f and fxx(2,1)fyy(2,1)&lt;fxy(2,1)2…

Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: 4y" – y = 0, У-2) %3D 1, у(-2) %3D -1

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Q: 1 If f(x, y,z)= of then x- y- 3z ду

A: Differentiate wrt y.

Q: 2 - Find the inter val on which f are Con Cave down and infleobion Points a -y = x2 5X+10 6- ソ= (¥+…

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Q: 5) Let z = f(x2 - y²). Show that y = 0 ду %3D ax

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Q: Suppose that w = f(x,y), x(s, t) = . = y(s, t) = And that fx(1,1) = 3, fy(1,1) = 4, fx(2,2) = 5,…

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