急,求函数y=sinx-cosx+sinxcosx - 知识问答

急,求函数y=sinx-cosx+sinxcosx的最大值,最小值

1个回答

y=sinx-cosx+sinxcosx
=sinx-cosx-1/2(1-2sinxcosx-1)
=sinx-cosx-1/2(sinx-cosx)^2+1/2
=-1/2(sinx-cosx-1)^2+1
=-1/2[2^0.5sin(x-Pi/4)+1]^2+1
Max=1
Min=-(2^0.5+1/2)

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