Find the point P on the graph of the function y=sqrt(x) closest to the point (9,0) The x coordinate of P is:

Answer 1

The shortest distance is on the normal (perpendicular) to the line pass through the point.

y = x^1/2

y' = 1 / 2x^1/2 this is the slope of the line

m = -2x^1/2 this is the slope of the normal

y = -2x^1/2(x - 9)

y = -2x^3/2 + 18x^1/2 this is the equation of the normal

x^1/2 = -2x^3/2 + 18x^1/2 this is the point of intersection

-17x^1/2 = -2x^3/2

-17 = -2x

8.5 = x (8.5, 8.5^1/2)

Now use the distance formula