问题
问答题
设f(x)在区间[0，1]上连续，在(0，1)内可导，且f(0)=f(1)=0，
，试证：
存在[*]，使f(η)=η。
答案
参考答案：
由题设，引入辅助函数φ(x)=x-f(x)，则φ(x)在[0，1]上连续，由已知条件f(1)=0及
，知φ(1)=1-f(1)=1＞0且
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设f(x)在区间[0，1]上连续，在(0，1)内可导，且f(0)=f(1)=0，，试证：
存在[*]，使f(η)=η。
参考答案：
由题设，引入辅助函数φ(x)=x-f(x)，则φ(x)在[0，1]上连续，由已知条件f(1)=0及，知φ(1)=1-f(1)=1＞0且
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