原题为英文班本:
suppose that both f and f' are differentiable on [0,+8), f(0)=f'(0)=0, and f''(x)>0for all x>0.
Prove that f(x)>0 for all x>0
三日内,请答案非常完善。谢谢啦
另外一道题
用中间值定理(mean value theorem)证明:
e^x>1+x+x^2/2+...x^n/n!, for all x>0 and 正整数n. (在n上面用归纳法induction)
谢谢了,答的很清楚,还有一道题不知道能不能帮忙做一下,实在麻烦了:
用中值定理(mean value theorem)证明:
e^x>1+x+x^2/2+...x^n/n!, for all x>0 and 正整数n. (在n上面用归纳法induction)
为什么f(n-1)(x)>0成立呢?
追答这是用数学归纳法啊,假设成立再推下一步