From the conclusion that has been proved above:

f'(ξ 1)=0，f'(ξ2)=0，

Then we know that F(ξ 1)=F(ξ2)=0.

According to Rolle theorem, ξ exists in (ξ 1, ξ2).

So F'(ξ)=0.

So: (f''(x)+[f'(x)]? )e^f(x)=0

Therefore, the conclusion has been proved.