Question

Find the point on the line y=2x+3 that is closest to the origin. I know I can use D^2=X^2+Y^2, and set S= d^2, then take the derivative of S to get minimun value. but should I use d not d^2 ??

Answer 1

It turns out, because distance is always positive, that if you minimize d^2 by taking a derivative, setting equal to zero and solving, the resulting value of x will also minimize d.

In short, because distance is always positive, minimizing d^2 will also minimize d at the same time.

Answer 2

OK, I can go alone with this. Still a little bit unclear. I want D, How can I use D^2 to replace what I want

Answer 3

Its just used to make the problem solution easier. Think of how much easier it is to take a derivative of:\[S=x^2+(2x+3)^2\]and set it equal to zero, than:\[d=\sqrt{x^2+(2x+3)^2}\]

Answer 4

Once you minimize d^2, take the square root to get the minimized value of d.

Answer 5

so ,you are saying, if my x, y can minimize d^2, I can also minimize d

Answer 6

yep.

Answer 7

thanks, got it