So I was solving a question -- Let $f $ be a real valued function on $R$ defined by $f (x)=xe^{-x} $. Suppose a line parallel to the x axis has distinct intersection points $P $ and $Q $ with the curve $y=f (x) $ Also $b $ is the value of $x $ for which $y=f (x) $ has a local maximum and $R$ be the intersection point of the line $x=b $ and the line $PQ $
Prove that $PR < RQ $
My Attempt So I tried to draw the graph of $y=xe^{-x} $ and then this statement seems pretty obvious. I was thinking that is there any other way to solve this question. Perhaps a one bit more mathematical. Also $b $ comes out to be equal to $1$
