What is the absolute max and min value?

Question

The function f(x, y, z)=(xyz)^1/2has an absolute maximum value and absolute minimum value subject to the constraint x+y+z=7 with x≥0, y≥0, and z≥0. Use Lagrange multipliers to find these values.

The absolute maximum value is _?

The absolute minimum value is _?

Answer 1

The function f(x, y, z)=(xyz)^1/2has an absolute maximum value and absolute minimum value subject to the constraint x+y+z=7 with x≥0, y≥0, and z≥0. Use Lagrange multipliers to find these values.

The absolute maximum value is 10sqrtr(30)/9

The absolute minimum value is 0