设g(x)在[a，b]连续，f(x)在[a，b]二阶可导，f(a)=f(b)=0，且对
【正确答案】正确答案：若f(x)在[a，b]上不恒为零，则f(x)在[a，b]取正的最大值或负的最小值． 不妨设f(x
0
)=
f(x)＞0，则x
0
∈(a，b)且f′(x
0
)=0，f″(x
0
)≤0
f″(x
0
)+g(x
0
) f′(x
0
)－f(x
0
)＜与已知条件矛盾．同理，若f(x
1
)=
f(x)＜0，同样得矛盾．因此f(x)≡0(
f(x)＞0，则x
0
∈(a，b)且f′(x
0
)=0，f″(x
0
)≤0
f″(x
0
)+g(x
0
) f′(x
0
)－f(x
0
)＜与已知条件矛盾．同理，若f(x
1
)=
f(x)＜0，同样得矛盾．因此f(x)≡0(
【答案解析】