设切点P（t,e^t) ,t≤1f'(x)=e^x斜率k=e^t,切线方程为y-e^t=e^t(x-t)x=0,得切线与y轴交点B（0,e^t(1-t))y=0,得切线与x轴交点A（t-1,0)∴ΔAOB面积S=1/2|OA|*|OB| =1/2*e^t*(t-1)^2S'=1/2*e^t*(t-1)^2+e^t*(t-1)=1/2(...