I see the graphs of these, using Geogebra, and I don't know how I can prove them..

1) Point A is @ (0,2) and point B is on the graph of y=x^2 + 1, what should be the approximate location of B so that the distance from A to B is as short as possible?

2) Point A is @ (3,1) and B is on a circle with center (1,2) and radius of 4. What is the closest point B should come to point A? Approximate to nearest thousandth.

And I'm having difficulty with this problem as well, but it doesn't use the same ideology of the above two.

A window is being built such that the bottom is a rectangle and the top is a semicircle. If there are 12 meter of framing material what should be the width of the window in order to let in the most light?

Any help is appreciated...