Try to discuss the monotonicity of function f (x) = x x 2 + 1
When ∵ x > 0, f (x) = XX2 + 1 = LX + 1x ≤ 12x · LX = 12, if and only if x = 1 "=" holds; when x ∈ (0, 1), f (x) is an increasing function, when x ∈ (1, + ∞), f (x) is a decreasing function; when x < 0, f (x) = XX2 + 1 = 1x + 1x ≥ 1 − 2 (− x) · 1 − x = - 12, if and only if x = - 1
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