Product & Quotient Rules of Differentiation

Posted: February 18, 2016 in Differential Calculus, Implicit Differentiation, The Derivative
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Having previously determined the derivative of ln(x), we now have that at our disposal to show one perspective of the product and quotient rules of differential calculus. A quick excursion to “implicit differentiation land” and a review of the chain rule will set things up nicely to meet our objectives here.

Product and Quotient Rules

Modified Product Rule

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.

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.