Use the method of Lagrange multipliers to maximize the function f(x,y,z)=4x+2y+z subject to the constraint x2+y+z2=1.

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Q: Use Lagrange Multipliers to solve the following: Maximize f(x, y, z) = 4x + 2y + z subject to r? + y…

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A: L(x,y)=f(a,b) +(x-a)fx(a,b)+(y-b)fy(a,b).

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A: To sketch the region of integration and then solve the given integral.

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A: The graph of the function fx

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Q: answer

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A: A detailed solution is given below.

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A: Given query is to find direction derivative.

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A: Here, given that: yc=c1x2+c2x3⇒y1=x2, y2=x3 And, u1=2x-3x2, u2=2x+3

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A: Given query is to find the value of y.