**Proof:** Clearly for

it is obvious that

. And since

is increasing on that interval it stands to reason that

. Lastly noting that

. We may finally deduce that the proposed inequality is definitely true for

/ Therefore let us restrict our attention to

. On this interval

and since

is decreasing on this interval we see that

. We need the following lemma.

**Lemma:** **Proof:** Let

. Then

and

and since

the conclusion follows.

Using this lemma and the previous deductinos we see that

. Now evaluating

gives us

and the result follows.