00:01
For this problem, we are asked to find the point on the graph of f of x equals x plus 1 squared that is closest to the point 53.
00:07
Now, technically, what we are asked to do here is essentially we are minimizing a distance function.
00:13
So that would be typically the square root of a x minus bx squared plus a y minus b y squared.
00:23
But if we have a minimum of the distance, that would also be a minimum of the distance squared.
00:28
So what we're trying to do then instead is minimize the function f of x, which would be given by if we have the point x f of x, then we would have x minus 5 squared plus f of x minus 3.
00:41
So minus x plus 1 squared minus 3 squared.
00:49
So then what i'll do here is do a little bit of rearrangement at this point.
00:57
So we can do this as.....