Find the point (x,y) on the curve y=sqrt(x+4) closest to the origin.

Answer 1

The distance from a point on the line from the origin is

((y-0)^2 + (x-0)^2)^0.5 =

(x^2+y^2)^.5 = (x^2 +(x+4)^0.5)

evaluate d/dx((x^2 +(x+4)^0.5)) = 0

This is the x value of the point closest to the origin, plug x into y = sqrt(x+4) to find the y value of this point