1.) Where 'a' is a positive real number use Fermat's adequating method to determine the max/min point(s) of f(x) = ax - x^3.
Next two problems: "Continuation of problem #1."
2.) Let a=12,make a large graph, and check the result from problem #1.
3.) Review your calculations in problem #I, and carefully explain the corresponding steps from the modern definition and use of the derivative.
4.) Using the same f(x) = ax - x^3, use Fermat's adequating method to determine the subtangent at x=1. Carefully show this subtangent ( label! ) on your graph from problem #2.
This question was asked on Mar 15, 2010.
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