Question

急急急，求函数y=sinx-cosx+sinxcosx的最大值，最小值

谢谢啦
注意公式sinx-cos=根2sin(4-派/4)可直接引用

Answer 1

y=sinx-cosx+0.5sin2x 连续可导，最值在极点处取
y'=cosx+sinx+cos2x=cosx+sinx+cos(^2)x-sin(^2)x=(cosx+sinx)(1+cosx-sinx)
y'=0时，x=0.75Pi+kPi或Pi+2kPi或0.5Pi+2kPi
代入可得，x=0.75Pi+2kPi时y=root(2)-0.5；x=0.75Pi+(2k+1)Pi时y=-root(2)-0.5；x=Pi+2kPi时，y=1；x=0.5Pi+2kPi时，y=1；
于是该函数最大值、最小值分别为1和root(2)-0.5

注释：
(^2)——平方
root()——根号
Pi——π
0.75——3/4
0.5——1/2

Answer 2

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)

Answer 3

借贵宝地做个任务