Consider the function f(x) = x 2 e −x , where x ∈ R. (
a) Use limits to describe the long-term behaviour of this function.
(b) Find all local maximum and minimum values of f(x).
(c) Find the x-coordinate of all points of inflection of the graph of f(x).
(d) Does f(x) have a global maximum? A global minimum?
(e) Draw the graph of f(x) indicating the main features, including any asymptotes, local maxima/minima, and points of inflection.
