Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x, y) = 4x + y Constraint: xy = 36 Minimum of f(x, y) = at (x, y) = (|
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- Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive.Minimize: f(x, y) = 2x + yConstraint: xy = 128Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x, y) = x2 + y2 Constraint: −2x − 4y + 5 = 0 Minimum of f(x, y) = at (x, y) =Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x, y) = x2 − y2 Constraint: x − 8y + 126 = 0
- Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.Minimize f(x, y, z) = x2 + y2 + z2Constraint: x + y + z − 27 = 0Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize f(x, y) = 2x + y Constraint: xy = 32Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.Maximize: f(x, y, z) = xyzConstraint: x + y + z - 6 = 0
- Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize f(x, y) = x2 − y2 Constraint: x − 2y + 6 = 0Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize f(x, y) = √(x2 + y2) Constraint: 2x + 4y − 15 = 0Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x, y) = x2 − 4x + y2 − 16y + 42 Constraint: x + y = 24 Minimum of f(x, y) = at (x, y) =
- Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Minimize f(x, y, z) = x2 + y2 + z2 Constraint: x + y + z = 1Use Lagrange multipliers to find the given extremum. Assume that x and y are positive. Minimize f(x, y) = 7x + y + 13 Constraint: x2y = 14 Minimum of f(x, y) = at (x, y) =