求函数f(x)=(3a-2)x^2+2x+1在[-3,2]上的最大值g(a)
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求函数f(x)=(3a-2)x^2+2x+1在[-3,2]上的最大值g(a)
求函数f(x)=(3a-2)x^2+2x+1在[-3,2]上的最大值g(a)
求函数f(x)=(3a-2)x^2+2x+1在[-3,2]上的最大值g(a)
首先a=2/3的时候,f(x)=2x+1,在x=2取到最大值5,所以g(2/3)=5
当a>2/3,f(x)开口向上,最大值在两端点处取到,f(-3)=27a-23,f(2)=12a-3
f(-3)>f(2) 等价于 a>4/3
f(-3)
(1)3a-2>0即a>2/3时
1° 2+1/(3a-2)>=(-1)/(3a-2)+3即a=<4/3时,g(a)=f(2)
2°2+1/(3a-2)<(-1)/(3a-2)+3即a>4/3时,g(a)=f(-3)
(2)3a-2<0即a<2/3时
1° 2+1/(3a-2)>(-1)/(3a-2)+3即a<4/3时,g(a)=f(-3)
2°2+1/(3...
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(1)3a-2>0即a>2/3时
1° 2+1/(3a-2)>=(-1)/(3a-2)+3即a=<4/3时,g(a)=f(2)
2°2+1/(3a-2)<(-1)/(3a-2)+3即a>4/3时,g(a)=f(-3)
(2)3a-2<0即a<2/3时
1° 2+1/(3a-2)>(-1)/(3a-2)+3即a<4/3时,g(a)=f(-3)
2°2+1/(3a-2)<(-1)/(3a-2)+3即a>4/3时,g(a)=f(2) 与a<2/3冲突,此情况不存在
(3)3a-2=0即a=2/3时 g(a)=f(2)=5
综上所述,当2/3 a<2/3或a>4/3时 g(a)=f(-3)=27a-23
a=2/3时 g(a)=5
希望对你有帮助!可以的话给点分哈!
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