Calculus 1 problem

[kentuckywildcat7373]

Hi I am new to this forum and was hoping for some guidance in figuring out one of my current calculus I problems.
a.) Let (a1 , a2 ) be a point in the plane. Consider the line L given by the points (x, x) as x ranges over all values of x. For what value of x is the point (x, x) closest to (a1 , a2 )?

b.) Given n numbers a1 , a2 , . . . , an , find the value of x minimizing the sum of squares (x−a1)^2 + (x− a2)^2 + · · · + (x − an )^2.
How is this related to Question A?

I guess the fact that there are not any numbers in the question is throwing me off. Any help that would get me on the right track would be greatly appreciated. Thanks!

 

[Bob Brown MSEE]

Did you do a)?
can we see your work?

 

[kentuckywildcat7373]

I was not able to do part a. Do I do the distance formula and then take a derivative and set it to zero?

 

[JeffM]

I was not able to do part a. Do I do the distance formula and then take a derivative and set it to zero?

Yes; that is certainly one way to solve this problem. Furthermore, I expect that the other way to do so will not be viewed as acceptable in a course on calculus. Set the derivative = zero and solve for x in terms of a_1 and a_2.