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
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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.
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samuelson mathxp 