设f(x)在[0,1]上三阶可导,f(0)=0,f(1)=1,f'(1/2)=0,求证:存在ξ∈(0,1),使|f′′′(ξ)|≥24

设f（x）在【0,1】上单调递增,f（0）>0,f(1) 设函数f(x)在闭区间[0,1]上可导,且f(0)×f(1) 设f(x)在[0,1]上有二阶连续导数,且满足f(1)=f(0)及|f''(x)| 设函数f(x)在（-∞,+∞)内有定义,f(0)不等于0,f(xy)=f(x)f(y),证明：f(x)=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)| 设函数f(x)=x-xlnx.证明f(x)在区间(0,1)上是增函数. 设f(x)=arctan x ,求f(0),f(-1),f(x^2-1) 设f(x)在R上满足f(x)的导数=2f(x),且f(0)=1,求函数f(x) 设f(x)在R上满足f(x)的导数=2f(x),且f(0)=1,求函数f(x) 设f(x)z [0,1]连续,f(x) 设函数f (x)在[0,1]上可导,且y=f (x)sin2x+f (x)cosx2,求 dy 设偶函数f(x)在大于0时为减函数,则不等式f(x)>f(2x+1) 设偶函数f(x)在大于0时为减函数,则不等式f(x)>f(2x+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