I am confused about a certain type of problem.
I was taught that when solving for a point on a plane (must use partial derivatives) say, $x+y+z=1$ that is closest to the origin, we are to minimize the square of the distance function, i.e. minimize $f(x,y)=x^2+y^2+z^2$.
But I don't understand the intuition of why we do this. How could we know that we should minimize the square of the distance formula, and not just the distance formula itself?