Find all values of such that
We’re invoking the same technique as in the problem here. Successively we have:
Obviously is differentiable in and its derivative is
It is . We distinguish cases:
- If then attains global maximum at equal to . Since it follows that .
- If then attains global minimum at equal to . In this case , however , the inequality cannot hold for all ; since is continuous its range is:
Hence this case is rejected.
- For the inequality obviously holds for all .
Summing up , .