Derive f(x) and f' (x) =- 1+e (-x)
When f'(x)=0, the value of x is 0 (because this is a fill-in-the-blank problem, that is, there must be a solution), and it can be directly substituted into x=0 to f (x) to get f(x).
Judging the existence of extreme value:
F'(x) is always positive on the left side and negative on the right side of x=0, so the left side increases and the right side decreases, and the maximum value is obtained when x=0.