Let f (x) be continuous on [0,2], have a second derivative in (0,2), and lim (x approaches 1 / 2) = 0,2 ∫ 1,1 / 2F (x) d (x) =It is proved that there is at least one point δ in (0,2) such that f (δ) = 0

Let f (x) be continuous on [0,2], have a second derivative in (0,2), and lim (x approaches 1 / 2) = 0,2 ∫ 1,1 / 2F (x) d (x) =It is proved that there is at least one point δ in (0,2) such that f (δ) = 0

2 ∫ [1 / 2,1] f (x) DX = f (2), using the integral mean value theorem, there exists η∈ (1 / 2,1), such that: 2 * (1 / 2) f (η) = f (2), that is, f (η) = f (2). In [η, 2], Rolle mean value theorem is applied to f (x), that is, there exists ξ 1 ∈ (η, 2), such that: F '(ξ 1) = 0 LIM (x -...)