Brain Teaser - Minimum distance between two curves

[CR Haeger]

(11-18-2015 06:40 PM)Jonathan Cameron Wrote:  

(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

You are close but I think you (correctly) solved for the x where the difference between f(x) and g(x) values are minimized. The x you provided is between the two x values that are the solution.

Hint: a line should be normal to both curves.