The derivative f' (x) = 2xe-x-x2e-x = (2x-x2) e-x.

∵e^-x>； 0

∴ When 2x-x2 >；; 0，f(x)>0

That is, when 0

Ⅶ when 2x-x 2 < 0, f (x)

That is, when x

∴

When x=0, f(x) takes the minimum value, and f(0)=0.

When x=2, f(x) reaches the maximum and f (2) = 4e-2.