拉格朗日中值定理求范围

问题描述:

拉格朗日中值定理求范围
a<=(1 sinx-cosx)/x在(0,派]上恒成立,求a的范围

(0,π]上a≤sinx-cosx=sin(x-π/4)/sqrt(2)
x-π/4∈(-π/4,3π/4]=>sin(x-π/4)∈(-1/sqrt(2),1]
=>sin(x-π/4)/sqrt(2)∈(-1/2,1/sqrt(2)]
=>a≤-1/2