f(x) = 根号3乘sin4x-cos4x
= 2(sin4xcosπ/6-cos4xsinπ/6)
= 2sin(4x-π/6)
最小正周期=2π/4=π/2
4x-π/6∈(2kπ-π/2,2kπ+π/2）,其中k∈Z时单调增
∴单调增区间：(kπ/2-π/12,kπ/2+π/6）,其中k∈Z
最大值2
此时4x-π/6=2kπ+π/2
x=kπ/2+π/6,其中k∈Z
4x-π/6