已知f(x)=1/2x-sinx(x属于R),则f(x)在区间(0,派)上最小值是?
问题描述:
已知f(x)=1/2x-sinx(x属于R),则f(x)在区间(0,派)上最小值是?
答
f'(x)=1/2-cosx=0,且x∈[0,π]
=>cosx=1/2
=>x=π/3
又f(0)=0,f(π)=π/2 ,f(π/3)=π/6 -√3/2
=>则f(x)在区间(0,派)上最小值是f(π/3)=π/6 -√3/2