f'(x)=e^x+a

f''(x)=e^x>； 0, f'(x) single increase,

Situation discussion:

( 1)a≤-e？ , on, f' (x) < 0, f(x) single subtraction,

f[ 1]≥0，f[2]≤0

e+a+b≥0

e？ +2a+b≤0

a≤-e？

A is on the horizontal axis and B is on the vertical axis. Draw a straight line l 1:e+a+b=0, l2:e? +2a+b=0，l3:a=-e？

L 1 above, below l2, to the left of l3, an empty area, a∑(-∞, -e? ]，b∈[-e+e？ ,+∞)

So a? +b？ , can approach ∞. There is no maximum value.

But there is a minimum, a=-e? ，b=-e+e？ ，a？ +b？ =e^4+e^4-2e？ +e？ =2e^4-2e？ +e？