设函数f(x)=x^2+(2a+1)x+a^2+3a(a属于R),若f(x)在[0,2]上最大值为0,求a

2025-04-07 15:56:48
推荐回答(1个)
回答1:

当-(2a+1)/2≤1即a≥-3/2时
f(x)max=f(2)=a�0�5+7a+6=0
故a=-6(舍去),a=-1

-(2a+1)/2>1,即:a<-3/2时,f(x)max=f(0)=a�0�5+3a=0.
故a=0(舍去)或a=-3.
综上得:a的取值为:a=-1或a=-3.