Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive. Minimize f(x, y, z) = x2 + y2 + z? Constraint: x + y + z – 18 = 0 f( ) =
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- 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 indicated extrema, assuming that x and y are positive.Minimize: f(x, y) = 2x + yConstraint: xy = 128Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Minimize f(x, y) = x2 − y2 Constraint: x − 2y + 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 − 5 = 0 f(______) = ________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, y, and z are positive. Minimize f(x, y, z) = x2 + y2 + z2 Constraint: x + y + z − 9 = 0
- Use 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 indicated extrema, assuming that x and y are positive. Minimize f(x, y) = x2 + y2 Constraint: x + y − 8 = 0Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive. Minimize f(x, y) = x2 − 10x + y2 − 14y + 28 Constraint: x + y = 10
- Use Lagrange multipliers to find the indicated extrema, assuming that x, and y are positive. Minimize f(x, y) = x2 − 10x + y2 − 14y + 28 Constraint: x + y = 20 f( ) =Use Lagrange multipliers to find the indicated extrema, assuming that x and y are positive. Maximize f(x, y) = 2x + 2xy + yConstraint: 2x + y = 100Use 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) =