问题标题：
y=sinx+cosx+sinxcosx+1的最值
问题描述：
y=sinx+cosx+sinxcosx+1的最值
冯在文回答：
y=sinx+cosx+sinxcosx+1
y'=cosx-sinx-(sinx)^2+(cosx)^2
=(cosx+1/2)^2-(sinx+1/2)^2
=(cosx+sinx+1)(cosx-sinx)
y'=0
=>sinx=cosxorcosx+sinx+1=0
=>tanx=1orsin(π/4+x)=-√2/2
=>x=π/4orx=π
maxy,atx=π/4
maxy=sinπ/4+cosπ/4+sinπ/4cosπ/4+1
=√2/2+√2/2+(√2/2)√2/2+1
=3/2+√2
miny,atx=π
miny=sinπ+cosπ+sinπcosπ+1
=0-1+(-1).0+1
=0
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