Brain Teaser - Minimum distance between two curves

[Jonathan Cameron]

(11-18-2015 04:35 PM)CR Haeger Wrote:  Finding the point on a curve closest to a fixed point off the curve seems to be fairly straightforward and often can be solved by hand. Finding the points on each of two curves which are closest seems to be a bit more involved.

Problem: What points on each of the two curves f(x) = x^2+1 and g(x) = √(x) are closest to each other?

x = cube root (1/16)

Hint: must be tangent point of both curves

-Jonathan