设f(x)在[0,1]上有连续的二阶导数,f(0)=f(1)=0,f(x)不恒为零.证明：max|f(x)|

设f(x)在[0,1]上有连续的二阶导数,f(0)=f(1)=0,f(x)不恒为零.证明：max|f(x)| 设f(x)在[0,1]上有连续导数,且f(x)=f(0)=0.证明 设f(x)在[0,1]上有连续的一阶导数,且｜f'(x)｜≤M,f(0)=f(1)=0,证明： 积分应用 设f (x)在[0,1]上具有二阶连续导数,若f ( π ) = 2,∫ [ f (x)+ f (x)的二阶导 设f(x)在[0,1]上具有二阶连续导数,且|f''(x)| 设函数f(x)在[0,b]上有连续的导数,且f(0)=0,记M=max|f'(x)|0 f(x)在点x=0处具有连续的二阶导数,证明f 设f(x)在[0,1]上有连续导数,f(0)=0,0 设f(x)在[a,b]上有连续的导数,且f(x)不恒等于0,f(a)=f(b)=0,证明∫(a,b)xf(x)f'(x) 设f(x)在区间【0,1】上有连续导数,证明x∈【0,1】,有|f(x)|≤∫(|f(t)|+|f′(t)|)dt 设函数f(x)有连续的二阶导数,且f '(0)=0,x趋近于0时,lim f ''(x)/|x|=1, 设函数f在[1]上存在二阶连续导数,且满足f(0)=f(1)=0,证明∫(1,0)f(x)dx=1/2∫(1,0)x(x