设f0(x)=x•ex,f1(x)=f′0(x),f2(x)=f′1(x),…,
问题:
设f0(x)=x•ex,f1(x)=f′0(x),f2(x)=f′1(x),…,fn(x)=f′n-1(x)(n∈N+).
(1)请写出fn(x)的表达式(不需证明);
(2)求fn(x)的极小值;
(3)设gn(x)=-x2-2(n+1)x-8n+8,gn(x)的最大值为a,fn(x)的最小值为b,求a-b的最小值.
设f0(x)=x•ex,f1(x)=f′0(x),f2(x)=f′1(x),…,fn(x)=f′n-1(x)(n∈N+).
(1)请写出fn(x)的表达式(不需证明);
(2)求fn(x)的极小值;
(3)设gn(x)=-x2-2(n+1)x-8n+8,gn(x)的最大值为a,fn(x)的最小值为b,求a-b的最小值.