Attachment 17056If you draw the graph, you have a cubic function

and a circle centred at (3,4) which touches the graph at a single point.

The radius of this circle is the minimum distance.

The point (x,y) where the circle meets the curve must satisfy

Hence

This is the distance of all points (x,y) on the curve from (3,4)

hence differentiating and setting the result to zero will find the x corresponding to minimum distance.