当x>0时,证明x-x3/6

题目

当x>0时,证明x-x3/6
是x的三次方除以6

答案

1.f(x)=sinx - x,f(0)=0,f '(x) = cosx -1 ≤ 0,f(x) 单减,
=> x>0时,f(x) g'(x) 单增
=》x>0时,g '(x) >0
=> x>0时,g (x)单增
=> x>0时,g (x)>0 即 x - x^3 /6 < sinx