已知函數(shù)f(x)=e
x-
ax
3(a為非零常數(shù)),記f
n+1(x)=f
n′(x)(n∈N),f
0(x)=f(x).
(1)當(dāng)x>0時(shí),f(x)≥0恒成立,求實(shí)數(shù)a的最大值;
(2)當(dāng)a=1時(shí),設(shè)g(x)=
,對(duì)任意的n≥3,當(dāng)x=t
n時(shí),y=g
n(x)取得最小值,證明:g
n(t
n)>0且所有點(diǎn)(t
n,g
n(t
n))在一條定直線上;
(3)若函數(shù)f
0(x),f
1(x),f
2(x)都存在極小值,求實(shí)數(shù)a的取值范圍.