试题与答案

设函数f(x)在闭区间[a,b]上连续,在开区间(a,b)内二阶可导,且f(a)=f

题型:问答题

题目:

设函数f(x)在闭区间[a,b]上连续,在开区间(a,b)内二阶可导,且f(a)=f(c)=f(b),其中c是(a,b)内的一点,且在[a,b]内的任何区间,上f(x)不恒等于常数.求证:在(a,b)内至少存在一点f,使f"(ξ)<0.

答案:

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