Find the distance from the origin to the closest point s on the graph of 14x 4xy 14y We begin by computing implicitly for points x y on the graph obtaining dy da We need to minimize the following function of a and y f x y There are four critical points located at the following x values listed in increasing order 21 202 003 1 Thus there is are x y and its distance from the origin is EB E 15 point s closest to the origin one of which is