题目

Treasure hunts (寻宝) have excited people’s imagination for hundreds of years both in real life and in books such a Robert Louis Stevenson’s Treasure Island. Kit Williams, a modern writer, had the idea of combining the real excitement of a treasure hunt with clues (线索) found in a book when he wrote a children’s story, Masquerade, in 1979. The book was about a hare, and a month before it came out Williams buried a gold hare in a park in Bedfordshire. The book contained a large number of clues to help readers find the hare, but Williams put in a lot of “red herrings”, or false cl已知函数f(x)=3sin(2x-π6)+2sin2(x-π12)．①求函数f（x）的最小正周期和单调递增区间；②若x∈[π4，π2]，求函数f（x）的最大值及取最大值时对应的x值．