Find Coordinates of Closest Point on y=sqrt(x) to (4,0)

[squenshl]

Homework Statement

Find the coordinates of the point $P(x,y)$ on the curve $y = \sqrt{x}$ that is closest to the point $(4,0)$.

Homework Equations

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!

 

[haruspex]

Do I then find the tangent line

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

 

[PeroK]

... And you need to draw a diagram.

 

[Mark44]

Homework Statement

Find the coordinates of the point $P(x,y)$ on the curve $y = \sqrt{x}$ that is closest to the point $(4,0)$.

Homework Equations

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!

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