[分析] 三次微分恆正,証一矩陣行列式為正

[burgerking07 (joy)]

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If a function f satisfies f'''>0 on the real line,
then for any t1< t2< t3< t4,
we have

        1          1          1           1
det (   t1         t2         t3          t4       ) >0 .    (証行列式值為正)
        t1^2       t2^2       t3^2        t4^2
        f(t1)      f(t2)      f(t3)       f(t4)


Thanks!
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P.S.
如果題目改成 f''>0, t1<t2<t3,
我可以証
       1      1        1
det (  t1     t2      t3     ) >0 ,
      f(t1)   f(t2)   f(t3)
不過上面題目還是証不出來.

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