Proof of Higher Mathematics Let f (x) be continuous on [0,1], derivable on (0,1), and f (1) = 0. Let f (1) = 0, then we try to prove that there is at least one point of ξ ∈ (0,1), so that f '(ξ) = - 2F (ξ) / ξ holds If the function f (x) is differentiable on [0,1], then there must be ξ ∈ (0,1) such that f '(ξ) = 2 ξ [f (1) - f (0)]

Proof of Higher Mathematics Let f (x) be continuous on [0,1], derivable on (0,1), and f (1) = 0. Let f (1) = 0, then we try to prove that there is at least one point of ξ ∈ (0,1), so that f '(ξ) = - 2F (ξ) / ξ holds If the function f (x) is differentiable on [0,1], then there must be ξ ∈ (0,1) such that f '(ξ) = 2 ξ [f (1) - f (0)]

Tips
1. Check the function x ^ 2 * f (x)
In [0,1], we can use the mean value theorem
2.f(x),g(x)=x^2
Using Cauchy mean value theorem

A proof of high number
Let f (x) be continuous on [0, π] and differentiable in (0, π). We prove the existence of ξ ∈ (0, π) such that f '(ξ) = - f (ξ) cot ξ

Let f (x) = sinxf (x)
F(0)=0 F(π)=0
Moreover, f (x) is continuous on [0, π], differentiable in (0, π), and satisfies the law of Lowe
Let f (ξ) = cos ξ f (ξ) + F '(ξ) sin ξ = 0
That is, f '(ξ) = - f (ξ) cot ξ

Proof of Higher Algebra
Let a and B be vectors of the geometric space V3, and prove that the set w = {Ka + LB | K, l ∈ r} is a subspace of V3 (A and B are vectors)
The case a and B are the same

First, we know that w is nonempty to any p belonging to W, then there are P1, P2, such that P = P1 * a + P2 * B & nbsp; KP = KP1 * a + KP2 * B, KP1, KP2 belong to R, then KP belongs to W, and Q belongs to w, then p + q = (P1 + Q1) a + (P2 + Q2) B also belongs to W, that is, P + Q belongs to W