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# Values of parameter

Find all values of such that

Solution

We’re invoking the same technique as in the problem hereSuccessively 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 , .