Minimize Distance Connecting 4 Towns

Posted: January 12, 2016 in Differential Calculus, Optimization, The Derivative
Tags: ,

Four towns (A, B, C, D) are situated to form a square with side length of 1 unit. Determine the minimum length of roadway that will link these four towns together.

View the James Grime video first.

Minimum Length

Click on the following link for an interactive exploration: GeoGebra

 

The graph below shows the length of roadways linking these towns as a function.

Length as a Function of  “x”

Four Towns Minimum

Click on the link provided here to determine local minimum.

 

Thanks for reading.

 

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