Use Lagrange multipliers to find the maximum and minimum values of ( f(xyz) = 5x²y⁴z ), subject to the constraint ( x²y²z² = 16 ), if such values exist.
Maximum:
a) ( 320 )
b) ( 400 )
c) ( 480 )
d) ( 560 )
Minimum:
a) ( -320 )
b) ( -400 )
c) ( -480 )
d) ( -560 )