Question

求函数f(x)＝5√3cos^2x+√3sin^2x-4sinx cosx在x∈【π/4,7π/24】的最小值.

Answer 1

cos^2x是什么意思?cos（2x）还是cosx的平方?说清楚

f(x)＝5√3cos^2x+√3sin^2x-4sinx cosx=4√3cos^2x-2sin2x+√3=2√3cos2x-2sin2x+3√3

=4cos(2x+π/3)+3√3

x∈[π/4, 7π/24]则有2x+π/3∈[5π/6, 11π/12]

最小值为f(7π/24)=4cos(11π/12)+3√3=-4cos(π/12)+3√3=3√3-√2-√6