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Optimal Values with Lagrange Multipliers<br>

Discover maximum and minimum values using Lagrange multipliers. Solve for constraints in functions of two and three variables. Enhance your mathematical knowledge today!<br>

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Optimal Values with Lagrange Multipliers<br>

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  1. 1. 2. 3. 4. Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f (x, y) = {image} , {image} • fmax = 750, fmin = - 750 • fmax = 0, fmin = - 30 • fmax = 30, fmin = - 30 • fmax = 750, fmin = 0

  2. 1. 2. 3. 4. 5. Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. f (x, y, z) = {image} , {image} = 1. • f (x, y, z) = {image} • f (x, y, z) = 0.7 • f (x, y, z) = {image} • f (x, y, z) = {image} • f (x, y, z) = 0.9

  3. 1. 2. 3. 4. Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. Then select the correct answer below. f (x, y, z) = 7 x - y - 6 z; x + 8 y - z = 0, {image} . • {image} • {image} • {image} • {image}

  4. 1. 2. 3. 4. Use Lagrange multipliers to find the shortest distance from the point (6, 10, 12) to the plane 6 x + 10 y + 9 z = 27. • D = 40 • D = {image} • D = {image} • D = 217

  5. Use Lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in plane x + 4 y + 2 z = 24. • V = 32 • V = 64 • V = 73 • V = 16

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