设f(x)在[0,1]上二阶可导,且f(0)=f(1),试证：至少存在一个§属于(0,1),使f''(§)=2f'(§)/(1-§)

微积分 设f(x)在[0,1]X上二阶可导,f(1)=f(0)=0设f(x)在[0,1]X上二阶可导,f(1)=f(0)=0,且max f(x)=2 (0 设函数f(x)在闭区间[0,1]上可导,且f(0)×f(1) 设函数f(x)在[0,1]上可导,且0 设函数f(x)在[0,1]上可导,且0 设f(x)在[1,e]上可导,且0 设f(x)在[0,1]上可积,且a 设f(x)在[0,1]上二阶可导,且f(0)=f(1),设F(x)=(1-x)*f(x),证明：存在§属于（0,1）使得F''(§)=0. 设f(x)在[0,1]上有二阶连续导数,且满足f(1)=f(0)及|f''(x)| 设f(x)在[a,b]上二阶可导,且f''(x)>0,证明:函数F(x)=(f(x)-f(a))/(x-a)在(a,b]上单调增加 设f(x)在[0,1]二阶可导,且f(x)在(0,1)上最大值为1/4,|f ''(x)| 设f(x)在[0,1]上具有二阶连续导数,且|f''(x)| 一道高数证明题,设函数f(x)在[0,1]上可导,且|f'(x)| 设f(x)在(0,1)具有二阶导数,且|f(x)| 设f(x)在[0,1]上连续,且f(x) 高等数学问题：设f(x)在[0,1]上连续,且f(x) 设f (x)在x=0处可导,且f (0)=0,求证：lim(x→∞)f (tx)-f (x)/x=(t-1)f' (0) 设函数f(x)在(-∞,+∞)可导,且满足f(0)=1,f'(x)=f(x),证明f(x)=e^x 设函数f(x)在(-1,1)有定义且满足x≤f(x)≤x²+x证明f'(0)存在且f'(0)=1