Problem
ALG-B2-M09-P002 Maximum product
#2
★★☆☆☆ Level 2 of 5
Let \(a,b,c>0\), \(a+b+c=9\). Find the maximum of \(abc\).
Hint. Apply AM-GM to \(a,b,c\).
By AM-GM, \(\sqrt[3]{abc}\le(a+b+c)/3=3\). Hence \(abc\le27\). Equality holds at \(a=b=c=3\).
Checks the classical maximum product with fixed sum.