Find the monotone interval and extremum of the following function, y = (x-1) (x + 1) ^ 3, y = 2 / 1 + x ^ 2

Find the monotone interval and extremum of the following function, y = (x-1) (x + 1) ^ 3, y = 2 / 1 + x ^ 2

y=(x-1)(x+1)^3
y'=(x+1)^3+3(x+1)^2(x-1)=(x+1)^2(x+1+3x-3)=2(x+1)^2(2x-1)
When x ∈ (- ∞, 1 / 2), f '(x) < 0, monotonically decreasing;
When x ∈ (1 / 2, + ∞), f '(x) > 0, monotonically increasing
Minimum f (1 / 2) = (1 / 2-1) (1 / 2 + 1) ^ 3 = - 27 / 16
Range [- 27 / 16, + ∞)
y=2/(1+x^2)
x^2≥0
1≤x^2+1＜+∞
0＜2/(1+x^2)≤2
Range (0,2]

Elden Ring Premiere

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