The problem involves finding the coordinates of a point on the curve defined by the equation \(y = \sqrt{x}\) that is closest to the point (4,0). This falls under the subject area of optimization in calculus.
The discussion is ongoing, with participants exploring different aspects of the problem, including the need to minimize distance and the role of the tangent line. Some guidance has been offered regarding the minimization of distance, but no consensus has been reached on the approach.
There is a repeated emphasis on the need to clarify the type of tangent line required and the importance of visual aids, indicating potential assumptions about the problem setup that may need further exploration.
Do you want a tangent that passes through the specified point or ... some other line?squenshl said:Do I then find the tangent line
You want to minimize the distance between ##(x, \sqrt x)## and (4, 0).squenshl said: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!