Question

一道数学题，急需，在线等

函数f(x)=根号3sinx-cosx(0<=x<=π)的最小值为

Answer 1

f(x) = (根号3)sinx - cosx
= 2 * ( (根号3)/2 * sinx - 1/2 * cosx)
= 2 * (sinxcosπ/6 - cosxsinπ/6)
= 2 * sin(x - π/6)
因为0<=x<=π
所以 -π/6 <= x - π/6 <= 5π/6
所以sin(x-π/6)当x = 0时有最小值sin(-π/6) = -1/2；当x - π/6 = π/2，也即x = 2π/3时有最大值1，

也即f(x)在x=0时取最小值-1，在x=2π/3时有最大值2。

Answer 2

提个2出来，再用辅助角公式化简

Answer 3

f(x)=√3sinx-cosx
= 2(√3/2*sinx-1/2*cosx)
= 2(cos(π/6)*sinx-sin(π/6)*cosx)
= 2sin(x-π/6)
又 0≤x≤π
所以 -π/6≤x-π/6≤5π/6
所以 2sin(x-π/6)∈[-1,2]
所以 最小值为 -1 当 x=0时取得