问答题
设f(x)在[0，+∞)可导，且f(0)=0．若f'(x)＞一f(x)，
【正确答案】正确答案：要证f(x)＞0 ←→ e
x
f(x)＞0 (x＞0)． 由e
x
f(x)在[0，+∞)可导且[e
x
f(x)]'=e
x
[f'(x)+f(x)]＞0 (x＞0) → e
x
f(x)在[0，+∞)单调上升 → e
x
f(x)＞e
x
f(x)｜
x=0
=0 (x＞0) → f(x)＞0 (x＞0)．
【答案解析】