Amazing Way to Graph the Gradient Function (Derivative)

It is likely that you have never seen this in all your schooling. Certainly, in our schools it seems to be an unknown skill.

Usually, when we are asked to draw a gradient function (graph of the derivative of a function), we are not asked for great accuracy.

We are expected to find the stationary points (locations of horizontal tangents). We are also expected to identify whether the gradient is positive or negative between each of those points of zero gradient. If the original graph has no identified points and no scale on the axes, any more detail than that is not required.

What you are about to see is a graphical/geometric method for drawing quite accurate gradient functions (graphs of derivatives), using a very simple geometric technique (parallel lines) and triangulation concept (gradient = rise/run).

I read about it many years ago in a publication of the NSW Department of Education called "The Mathematics Teacher." The contributer was G I Miller from Corowa (near the NSW/Victorian border). I tried to find out more about this person but could not. I think he deserves some cudos for having shared this method.

You may download a PDF copy of his article from my website via this link: http://www.crystalclearmaths.com/wp-c....


If you also wish to have a useful collection of functions to practise your differentiation skills, I have created a FREE PDF FILE containing a wide variety of exercises (and their solutions). You might like to work through them either on your own or with friends. You may download the file from here: http://www.crystalclearmaths.com/wp-c....

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Best wishes for your study and your mathematics!

Thank you.