Problem:
Let be a smallest value of the function
. Prove that
when
.
Proof:
For ,
.
From this, we see that for
and
. Consequently,
attains its maximum value in the interval
. On this interval
So, . But,
As , the first term on the right hand side tends to the limit
. In the second term, the factor
of the numerator tends to zero because
.
So,
auf wiedersehen,
Nalin Pithwa.
Reference: Nordic Mathematical Contest, 1987-2009.