To answer Section 1.6, number 2, if you don't have a graphing calculator, you can get a fair idea of what's going on by going to this website: Javascript Function Evaluatory.
As in this problem, you could play around with the gridlines to zero-in on the low point, but if I were a student, I would just minimize the parabola living inside the square root, on the principle that the square root is minimized when what's inSIDE it is minimized, and we know quite a bit about minimizing paraboloas (or we soon shall, in Chapter 2!).
In this first picture, you see the square root function, and I've drawn a line segment in blue from the point on that square root function that is closest to the point (2, 0).
In the second picture, below, you see the distance function superimposed over the previous graph, and you see that its low point occurs at the same point that the distance from the square root function to
(2, 0) is minimized, which, now that you see it, maybe it makes sense. These are hard to have any intuition about, until somebody just flat-out shows you...
I'm using a Computer Algebra System (CAS) called Maple, which is a pretty high-dollar piece of software, to render these pictures. But the point, here, and the reason I don't mind working this out, is even if you DON'T have a graphing calculator and DON'T break down and use that grapher on the Hofstra.edu site that's linked, above, you can STILL do some pretty powerful analysis on this problem, with paper and pencil, once you see how I'm reasoning, here...
I'd still advise any student in this class to get a TI-83 or a TI-84 and learn how to use it, if that student wanted to optimize the learning experience. We'll muddle through, if we have to, but... There's so much quick insight you can gain by being able to crank out a quick graph. I like including these "borderline" questions (Graphing Calculator or Analysis Genius), for their enrichment potential.
FYI, the following is one way to reason out what the distance function must look like. I leave the simplification of the mess inside the radical (in other words, the simplification of the radicand), to the student, as an exercise.