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!
The equation for finding the coordinates of the closest point on y=sqrt(x) to (4,0) is (4,2).
To find the distance between two points on a graph, you can use the distance formula: d = √[(x2-x1)^2 + (y2-y1)^2]. In this case, the points are (4,0) and (4,2).
The process for finding the closest point on a graph to a given point involves finding the distance between the given point and all other points on the graph, and then selecting the point with the smallest distance.
Finding the closest point on a graph is useful for determining the shortest distance between a point and a curve or line, as well as for optimization problems in which the closest point represents the optimal solution.
Yes, this equation can be used for any type of graph as long as the y-coordinate can be expressed as a function of the x-coordinate. However, the specific coordinates of the closest point will vary depending on the shape and position of the graph.