f(X)=In(sinx)在[π/6,5π/6]上满足罗尔定理的值?
问题描述：
f(X)=In(sinx)在[π/6,5π/6]上满足罗尔定理的值?
求满足罗尔定理的ξ
答
答：
f(x)在[π/6,5π/6]满足罗尔定理时,有：
f'(ξ)=0 ,ξ∈(π/6,5π/6)
f'(ξ)=cosξ/sinξ=cotξ
当ξ=π/2∈(π/6,5π/6)时,f'(ξ)=0
此时f(π/2)=ln1=0
所以满足罗尔定理的x为π/2,f(x)为0.