f(x)为偶函数,故只需考虑x∈[0,5]
f(x)=-x²+3x=-(x-1.5)²+2.25 0≤x≤3
开口向下,x=1.5时,f(x)取得最大值=2.25
f(x)=-x²+(a+3)x-3a=-[x-(a+3)/2]²+(a+3)²/4-3a 3 开口向下,对称轴x=(a+3)/2 当(a+3)/2≤3→a≤3时,区间(3,5]在对称轴右侧,f(x)单调递减f(x) g(a)=2.25 3≤(a+3)/2≤5→32.25→a>6时, g(a)=(a-3)²/4 当a>7时,区间(3,5]在对称轴左侧,f(x)单调递增f(x) g(a)=2a-10
整理g(a)=2.25 a≤6
g(a)=(a-3)²/4 6
g(a)=2a-10 a>7