设x∈[π/4,π/3].f(x)=1/4(sin2x-cos2x-(√3)/2)+(√3)/2)sin2(x-π/4)求f(x)的最值
问题描述:
设x∈[π/4,π/3].f(x)=1/4(sin2x-cos2x-(√3)/2)+(√3)/2)sin2(x-π/4)求f(x)的最值
【加号】的前后分别为一个式子(这里括号忘记了)
答
=√2/4sin(2x-π/4)-√3/8+√3/2sin(2x-π/4)=(√2+2√3)/4sin(2x-π/4)-√3/8x∈[π/4,π/3].π/4≤2x-π/4≤5π/12sin(2x-π/4)∈[√2/2,(√2+√6)/4]最小值=(2+2√6-√3)/8最大值=(1+√6+3√2)/8...