So no verticle asymptote, what about an arrowhead?You can draw it anyway that makes it clear to you. But most people would not say that there is a global max at -infinity since it's not really a point on the line. Similarly, no vertical asymptote there.
Also can you please confirm is this is correct.
lim -> -infinity = -infinity because x²e^(-ax) ->0 and
lim->infinity = 0 because x²e^(-ax) ->0