f(x)=-x2+6x-3(0

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f(x)=-x2+6x-3(0f(x)=-x2+6x-3(0f(x)=-x2+6x-3(0抛物线开口向下,对称轴为:x=3f(x)在[0,4)上先增后减,且减区间短,增区间长,所以函数的最大值f(ma

f(x)=-x2+6x-3(0
f(x)=-x2+6x-3(0

f(x)=-x2+6x-3(0
抛物线开口向下,对称轴为:x=3
f(x)在[0,4)上先增后减,且减区间短,增区间长,所以函数的最大值f(max)=f(3)=6
最小值为f(0)=-3
所以原函数的值域为:
[-3,6]

f(x)=-(x^2-6x+3)=-(x^2-6x+9-6)=-(x-3)^2+6
f(3)=6
f(0)=-3
0<=x<4 -3<=f(x)<=6