设f(x)在x
0
的邻域内四阶可导，且｜f
4
(x)｜≤M(M＞0)．证明：对此邻域内任一异于x
0
的点x，有
【正确答案】正确答案：由f(x)=f(x
0
)+f'(x
0
)(x－x
0
)+
f(x')=f(x
0
)+f'(x
0
)(x'－x
0
)+
两式相加得 f(x)+f(x')－2f(x
0
)=f''(x
0
)(x－x
0
)
2
+
f(x')=f(x
0
)+f'(x
0
)(x'－x
0
)+
两式相加得 f(x)+f(x')－2f(x
0
)=f''(x
0
)(x－x
0
)
2
+
【答案解析】