Brain Teaser - Minimum distance between two curves

[Jonathan Cameron]

(11-18-2015 07:06 PM)CR Haeger Wrote:  

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

Oops! I made an implicit assumption that the slopes would be equal at the same x. When I got rid of that assumption, I get a gory polynomial -- which I have not solved yet...