0232565

假设$\forall x \in \left( {a, + \infty } \right),f'\left( x \right) \ne 0$,则由$\bf{Darboux定理}$知,$f'\left( x \right)$恒正或恒负

不妨设$f'\left( x \right)$恒正,则$f\left( x \right)$严格单调增加,于是
\[f\left( x \right) > f\left( {a + 2} \right) > f\left( {a + 1} \right) > f\left( y \right),\forall x > a + 2,y \in \left( {a,a + 1} \right)\]

从而可知\[\mathop {\lim }\limits_{x \to \begin{array}{*{20}{c}}
{ + \infty }
\end{array}} f\left( x \right) \ge f\left( {a + 2} \right) > f\left( {a + 1} \right) \ge \mathop {\lim }\limits_{x \to \begin{array}{*{20}{c}}
{{a^ + }}
\end{array}} f\left( x \right)\]

这与题设条件矛盾