f(x)在[0,1]上连续,在(0,1)内可导,f(0)=0,|f'(x)|

Question

f(x)在[0,1]上连续,在(0,1)内可导,f(0)=0,|f'(x)|

Answer 1

楼上证明饶了一个大弯子.
本题可用用Lagrange中值定理来证
设x0属于[0,0.5] 且| f(x0)|是[0,0.5]上的最大值,则：
|f(x0)|=|f(x0)-f(0)|