因为x属于[-π/6,π/3]
所以2x属于[-π/3,2π/3]
(2x+π/6)属于[-π/6,5π/6]
设t=(2x+π/6),t属于[-π/6,5π/6]
f(x)=2sint
由单调性知:最小值为f(-π/6)=-1
最大值为f(π/2)=2
因为x属于[-π/6,π/3]
所以2x属于[-π/3,2π/3]
(2x+π/6)属于[-π/6,5π/6]
设t=(2x+π/6),t属于[-π/6,5π/6]
f(x)=2sint
由单调性知:最小值为f(-π/6)=-1
最大值为f(π/2)=2