Find the point on the graph of f (x) = √x that is closest to the point (4, 0).

Answer 1

The shortest distance shall be on a normal (perpendicular) to f(x).

The normal has a slope that is the negative reciprocal of the slope of f(x)

f'(x) = 1 / 2√x

Slope of normal is -2x

Use two-point form to determine equation of normal.

Determine point of intersection of normal and f(x).