Let f (x) be derivative of second order, f '' (x) > 0, f (0) = 0. It is proved that f (x) = f (x) / x, X ≠ 0, f (x) = f (0), x = 0 is monotone increasing function

Let f (x) be derivative of second order, f '' (x) > 0, f (0) = 0. It is proved that f (x) = f (x) / x, X ≠ 0, f (x) = f (0), x = 0 is monotone increasing function

If we prove that f '(x) = (XF' (x) - f (x)) / X & # 178; > 0, that is, XF '(x) - f (x) > 0 (1)
1. When x > 0, f '(ξ 1) = [f (x) - f (0)] / (x-0), where 0

F (x) is continuous on [0,1], definite integral f (x) DX = 0, it is proved that there is at least one point ξ, such that f (1 - ξ) = - f (ξ)
Definite integral [0,1]

Let x = 1-T so 0

Given that the graph of function y = x3-3x + C has exactly two points in common with X axis, then C = ()
A. - 2 or 2B. - 9 or 3C. - 1 or 1D. - 3 or 1

The derivative function can be y ′ = 3 (x + 1) (x-1) if y ′ > 0, then x ＞ 1 or X ＜ - 1; if y ′ < 0, then - 1 ＜ x ＜ 1; the function increases monotonically on (- ∞, - 1), (1, + ∞), and decreases monotonically on (- 1,1). The maximum value of the function is obtained at x = - 1, and the minimum value is obtained at x = 1