It is known that the function f (x) = KX + bx2 + C (C ＞ 0 and C ≠ 1, K ＞ 0) has a maximum point and a minimum point, and one of the extreme points is x = - C (1). Find another extreme point of function f (x). (2) let the maximum of function f (x) be m and the minimum be m. if M-M ≥ 1 is constant for B ∈ [1, 32], find the value range of K

It is known that the function f (x) = KX + bx2 + C (C ＞ 0 and C ≠ 1, K ＞ 0) has a maximum point and a minimum point, and one of the extreme points is x = - C (1). Find another extreme point of function f (x). (2) let the maximum of function f (x) be m and the minimum be m. if M-M ≥ 1 is constant for B ∈ [1, 32], find the value range of K

(1) When f ′ (x) = − kx2 − 2bx + CK (x2 + C) 2 = 0, x1 ·x2 = - C ∵ x = - C is one of the extremum points, and the other extremum point is 1 (2). From F ′ (− C) = 0, k = 2BC − 1. From (1), we can see that f (x) is a decreasing function in - ∞ - C), an increasing function in (- C, 1), and a decreasing function in (1, + ∞)