Let . Find the maximum vale of the function

**Solution**

Using the AM – GM inequality we have

Hence,

Equality holds when

Since there exists an such that the equation has at least one root. The minimum follows.

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Let . Find the maximum vale of the function

**Solution**

Using the AM – GM inequality we have

Hence,

Equality holds when

Since there exists an such that the equation has at least one root. The minimum follows.