if f(x)=(x^2)( e^-2x) then f is increasing for all x such that?

Answer 1

f'(x) = 2xe^-2x - 2x²e^-2x > 0; 2x(1 - x)e^-2x > 0. Because e^-2x > 0 for all real numbers we have inequality

x(1-x) > 0 and solution (0, 1). Only here f(x) increasing