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Use the method of Lagrange multipliers to find the maximum and minimum values of F(x,y,z) =...

Use the method of Lagrange multipliers to find the maximum and minimum values of F(x,y,z) = 5x+3y+4z, subject to the constraint G(x,y,z) = x2+y2+z2 = 25. Note the constraint is a sphere of radius 5, while the level surfaces for F are planes. Sketch a graph showing the solution to this problem occurs where two of these planes are tangent to the sphere.

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