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2. (a) Let a,b ≥0. Define the function f by f(x)=(a+b+x)/3-∛abx Determine if f has a...

2. (a) Let a,b ≥0. Define the function f by f(x)=(a+b+x)/3-∛abx Determine if f has a global minimum on [0,∞), and if it does, find the point at which the global minimum occurs.

(b) Show that for every a,b,c≥0 we have (a+b+c)/3≥∛abc with equality holding if and only if a=b=c. (Hint: Use Part (a).)

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