Question

Find the point on the graph of √(x+1) that lies closest to point ( 4,0).

Answer 1

What problem are you having with that?

Answer 2

Overall concept: Substitute points into the distance formula find a minimum using derivatives.
\[d=\sqrt{(x _{2}-x _{1})^{2}+(y _{2}-y _{1})^{2}}\]where\[(x _{1}, y _{1})=(4,0)\]\[(x _{2},y _{2})=(x, \sqrt{x+1})\]Simplify. Take the derivative. Find critical points by setting the derivative to zero. Determine if there is a relative minimum and what it is. Plug that back into the original function to find the y value of the point.