y=（sinx+cosx)平方+2cos平方x
=sin^2x+2sinxcosx+cos^2x+2cos^2x
=1+sin2x+cos2x+1
=√2(sin2xcosπ/4+cos2xsinπ/4)+2
=√2sin(2x+π/4)+2
所以递增区间是
2kπ+π/2>=2x+π/4>=2kπ-π/2
2kπ+π/4>=2x>=2kπ-3π/4
kπ+π/8>=x>=kπ-3π/8
最大值是√2+2
最小值是-√2+2