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#### DeusAbscondus

##### Active member

- Jun 30, 2012

- 176

I am seeking to hone my skills & deepen my knowledge and understanding of the relationship between f(x) and f'(x) and f''(x)

To this end, I have made a workhorse cubic with four sliders (using geogebra) attached to co-efficients a, b, c and d respectively.

My study plan is to hide f(x), manipulate the sliders (values of co-efficients) thus transforming f(x) in various ways, then trying to deduce what f(x) must now look like and trying to sketch it myself.

Two questions occur to me:

1. How can I best systemize any learnings thereby gained, in terms of rules of transformation which I can formulate, as I manipulate the co-efficients? and,

2. What principles do I need to arrive at to be a good sketcher of f(x) from f'(x)

Thanks for any help, suggestion or directions you can offer.

PS I have included inline a screenshot of the geogebra worksheet I have made and would also welcome any comments as to any errors to correct, areas of obvious improvement etc

PSS I have asked identical question in geogebraforum and am awaiting a response.