Multivariable Calculus Question - Global max & min

Question

Find the global maximum and minimum to the function f (x,y,z) = xy²z³ on the set S = (x, y, z) : x² + y² + z² ≤ 1 .

Answer 1

Hi.

x² + y² + z² = 1 .represents a sphere that center is origin and radius is 1

x² + y² + z² ≤ 1 . represents all points inside and on the above sphere

so the min is center and max is all points are on the sphere.

I hope it is useful,

Minoo