## Posts Tagged ‘Optimization Problem’

The main subject of this entry was originally planned as an optimization problem involving differential calculus only; its been slightly modified. This more interesting approach provides the derivative up front, presenting students with three separate tasks to pursue from that point. As a consequence, students are reintroduced to differential equations and curve sketching.

A talking point emerges as well: Is there a difference between derivatives and differential equations?

Inscribed Triangle of Maximum Area

Click on the link provided here to explore area of the inscribed triangle.

Thanks for looking.

## 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.

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”

Click on the link provided here to determine local minimum.

Thanks for reading.

## Maximize Triangle Area (Putnam problem)

Posted: January 12, 2016 in Calculus: An Introduction, Integral Calculus, The Derivative
Tags: , , ,

Determine a position “c” in terms of “a” and “b” that will result in triangle ABC having maximum area. Prove that the areas bounded by f(x) and the line segments AC & BC at that position are equal.

Click on the link provided here to explore the triangle area above.