Given the function f (x) = & # 188; X & # 8308; = & # 8531; ax & # 179; - A & # 178; X & # 178; + A & # 8308; (a > 0), find the monotone interval of the function

Given the function f (x) = & # 188; X & # 8308; = & # 8531; ax & # 179; - A & # 178; X & # 178; + A & # 8308; (a > 0), find the monotone interval of the function

It is necessary to seek the derivative
f’（x）=x^3+ax^2-2ax=x(x+2a)(x-a)
Because a > 0, the three stationary points of F (x) are x = - 2A, x = 0, x = a
When x ≤ - 2, f '(x) ≤ 0, so in (- ∞, - 2A] is a monotone decreasing function
When - 2A ≤ x ≤ 0, f '(x) ≥ 0, so in [- 2A, 0] is a monotone increasing function
When 0 ≤ x ≤ a, f '(x) ≤ 0, so it is a monotone decreasing function in [0, a]
When x ≥ a, f '(x) ≥ 0, so in [a, + ∞) is a monotone increasing function