FERMAT "DERIVATIVE" PROBLEMS

1. Use FERMAT'S adequating method to determine the max/min point(s) of f(x)=ax-x^3, where a is a positive real number.

2. (continuation of 1) Let a=12, make a large graph, and check the result from problem 1.

3. (continuation of 1) Review your calculations in problem 1, 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 (labels!) on your graph from problem 2.

1. Use FERMAT'S adequating method to determine the max/min point(s) of f(x)=ax-x^3, where a is a positive real number.

2. (continuation of 1) Let a=12, make a large graph, and check the result from problem 1.

3. (continuation of 1) Review your calculations in problem 1, 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 (labels!) on your graph from problem 2.

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