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Let

, for

. For any

. Moreover:

1. If

, then

is strictly increasing.

2. If

, then

is strictly decreasing.

3. If

, then

has exactly one local minimum and it is the absolute minimum.

Reference: C. X. Kang and E. Yi, "The convergence behavior of

," The College Mathematics Journal, 38(5), 2007 pp. 385–386.

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The Convergence Behavior of a One-Parameter Family