Given a ∈ R, function f (x) = x | x-a |, problem (1) when a = 2, write the monotone increasing interval of function y = f (x) (2) find the maximum value of the function y = f (x) in the interval [0,2]

Given a ∈ R, function f (x) = x | x-a |, problem (1) when a = 2, write the monotone increasing interval of function y = f (x) (2) find the maximum value of the function y = f (x) in the interval [0,2]

When x > = 2, f (x) = x ^ 2-2x, f (x) increases on the right side of x = 1, so the monotone increasing interval is (2, infinity)
When x

Finding monotone increasing interval of function y = Log1 / 2 (1 / 2cos2x)

Solution
y=1+log1/2 cos 2x
The monotone increasing interval of COS 2x is (- π / 4 + K π, K π)
The monotone decreasing interval of is (K π, π / 4 + K π) k ∈ Z
So the monotone increasing interval of the function is (K π, π / 4 + K π)
The monotone decreasing interval is (- π / 4 + K π, K π) k ∈ n*

It is proved that the function f (x) = 2 + X Fen 1 (0, + infinity) is monotonically decreasing on

Let x1 ∈ (0, + ∞) and X2 ∈ (0, + ∞), where x10,2 + X1 > 0,2 + x2 > 0
So f (x1) - f (x2) > 0, so f (x) is a decreasing function at (0, + ∞)