find interval for which the function f(x)=xex(1-x) is increasing or decreasing function

differentiate the given equation

you get e^x(1-x) + (xe^x(1-x))*(1-2x)

this can be written as (e^x(1-x) )*[1+x - 2x^2]

this equation is +ve if 1+x - 2x^2) is >0

this equation is positive in (-ve infinity to -1/2)....union  ......(1 to +ve infinity)