Finding a Coordinate

1. Dec 2, 2017

squenshl

1. The problem statement, all variables and given/known data
Find the coordinates of the point $P(x,y)$ on the curve $y = \sqrt{x}$ that is closest to the point $(4,0)$.

2. Relevant equations

3. The attempt at a solution
The derivative is $y'(x) = \frac{1}{2\sqrt{x}}$. Do I then find the tangent line to $y = \sqrt{x}$. A little help would be great!!!

2. Dec 2, 2017

haruspex

Do you want a tangent that passes through the specified point or .... some other line?

3. Dec 2, 2017

PeroK

... And you need to draw a diagram.

4. Dec 2, 2017

Staff: Mentor

You want to minimize the distance between $(x, \sqrt x)$ and (4, 0).