Question

已知函数f(x)=x^2+2xsina-1,x∈[-√3/2,1/2] 1.当a=π/6时,求f(x)的最大值和最小值

Answer 1

(1)a=π/6,则f(x)=x²+√3x-1=(x+√3/2)²-7/4

∴f(x)在(-∞,-√3/2)单调减,(√3/2,+∞)单调增

又x∈[-√3/2,1/2]

∴f(x)在定义域单调增

当x=-√3/2时,f(x)min=-7/4

当x=1/2时,f(x)max=(2-√3)/4

(2)

f(x)=x²+2sina x-1=(x+sina)²-1-sin²a

∴f(x)在(-∞,-sina)单调减,(-sina,+∞)单调增

要满足f(x)在[-√3/2,1/2]单调

则1/2