Find interval for which the function f(x)=xe^{x(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)