Minimizing Area
geometry
There is a rectangle and a path that goes from the bottom-left corner to the top-right. The path can only move upwards or towards the right. Draw a vertical line L through the rectangle. Now look at the area under the curve to the left of L, and the area above the curve to the right of L. Call this total area A_L. In the example figure below, L is the dotted line and A_L is the shaded area.
What is the line L that minimizes A_L?
