What is the absolute maximum value and the absolute minimum value?

Question

The function f(x,y,z)=(xyz)^1/2 has an absolute maximum value and absolute minimum value subject to the constraint x+y+z=3 with x≥​0, y≥​0, and z≥0. Use Lagrange multipliers to find these values.

Fill in the blank

The absolute maximum value is __. The absolute minimum value is ___.

Answer 1

Lagrange multiplier allows the creation of a system of simultaneous equations formed by ...

Fx=AGx ... .5(yz)^-.5 =A

Fy=AGy ... .5(xz)^-.5=A

Fz=AGz ... .5(xy)^-.5=A

Note from the above x=y=z ... Use this fact solve G for x=y=z =1 ... this will be the absolute maximum value of F. The absolute minimum value will be zero.