Posts Tagged ‘Optimization Problem’

Inscribed Triangle: Maximum Area

Posted: March 11, 2016 in Calculus: An Introduction, Curve Sketching, Differential Calculus, Differential Equations, Optimization, The Derivative
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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

Inscribed Triangle animation

 

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
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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.

 

Maximize Triangle Area (Putnam problem)

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

Putnam Area

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