00:01
For this problem, we are asked to find the point on the graph of f of x equals x squared that is closest to the point to one -a -half.
00:07
Now, technically, what we are being asked to do is to minimize the distance function, which, you know, if we were given points, if we have two points, a -b and c -d, then we would want not a -minus b squared.
00:22
It would be, for instance, a -minus c squared plus b -d -d -squared.
00:29
But dealing with that square root is going to be a little bit painful.
00:34
So what we can do instead is minimize d squared.
00:39
A minimum of d squared should also correspond to a minimum of d.
00:42
So what we'll find now is that what we're trying to do is minimize the point x, or minimize the function, x minus 2 squared, plus x squared minus 1ā2 squared.
00:57
So that is our f of x that we're trying to minimize...