求个最大值 (t-2/3√3)²/(3t²-1)(t-2/3根号3)²/(3t²-1)另外 类似的函数的最值怎么解?范围是 (根号3,5/3根号3)

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求个最大值(t-2/3√3)²/(3t²-1)(t-2/3根号3)²/(3t²-1)另外类似的函数的最值怎么解?范围是(根号3,5/3根号3)求个最大值(t-2

求个最大值 (t-2/3√3)²/(3t²-1)(t-2/3根号3)²/(3t²-1)另外 类似的函数的最值怎么解?范围是 (根号3,5/3根号3)
求个最大值 (t-2/3√3)²/(3t²-1)
(t-2/3根号3)²/(3t²-1)
另外 类似的函数的最值怎么解?
范围是 (根号3,5/3根号3)

求个最大值 (t-2/3√3)²/(3t²-1)(t-2/3根号3)²/(3t²-1)另外 类似的函数的最值怎么解?范围是 (根号3,5/3根号3)
答:


设:
k=(t-2/3√3)²/(3t²-1)
=(t²-4t/3√3+4/27)/(3t²-1)
整理:
3kt²-k=t²-4t/3√3+4/27
(3k-1)t²+4t/(3√3)-k-4/27=0
方程有解,则有:
判别式=(4/3√3)²+4(3k-1)(k+4/27)>=0
所以:4/27+3k²+4k/9-k-4/27>=0
3k²-5k/9>=0
k<=0或者k>=5/27
所以:极大值为0,极小值为5/27