Question

Find the point on the curve y = sqrt (x) that is closest to the point (5,0). Please type in only the exact values for x and y, separated by a comma. You should not enter any parentheses as they are already included below. (x, y) =

Answer 1

The given curve is

All the points on the curve are of the form (x, x^1/2).

Let D be the distance from the point (x, x^1/2) to (5, 0). Then,

As we are looking for the closet point, our aim is to minimize D.

To minimize D, first we have to find the critical point(s) by setting D'(x) to 0.

So, the only critical point is at x = 9/2.

As D'(x) changes its sign from negative to positive at x = 9/2, there is a local minimum at that point.

Hence, the closest point on the curve to the point (5, 0) is