f(x)=a(sinx-cosx)的平方+2(sinx+cosx)的最小值和最大值~恕我问一个比较蠢的题目~

f(x)=a(sinx-cosx)的平方+2(sinx+cosx)的最小值和最大值~恕我问一个比较蠢的题目~
f(x)=a(sinx-cosx)的平方+2(sinx+cosx)的最小值和最大值~
恕我问一个比较蠢的题目~

f(x)=a(sinx-cosx)的平方+2(sinx+cosx)的最小值和最大值~恕我问一个比较蠢的题目~
f(x)=a(sinx-cosx)^2+2(sinx+cosx) = a - 2asinxcosx +2(sinx+cosx)
令 t=sinx+cosx
则 t=√2sin(x+π/4) ,所以 -√2≤t≤√2
而 t^2 = 1+2sinxcosx,即 2sinxcosx = t^2-1
所以
f(x) = a -a(t^2-1)+2t= -at^2 +2t +2a
·若a=0时
f(x)的最大值为 max = 2√2,最小值为min=-2√2
·若a≠0时
f(x)=-at^2 +2t +2a = -a(t-1/a)^2 +2a+1/a
下面再分情况讨论.
·当a>0时（开口向下）
(1) 0

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