Differentiation from First Principles

The Resource: https://goo.gl/NRq3fc

This is my worksheet which helps pupils to discover the rules for differenting polynomials.

I’d use this after an introductory discussion of a problem in which the gradient of a curve is sought. Often I’ve asked “How would you work out Usain Bolt’s speed 20m into a race?” This usually leads to a discussion about how speed guns work.. I inevitably sketch a distance time graph and we talk about how to find the gradient at a point. Tangents are often suggested and I may have to push students towards the idea of chords and limits, perhaps unsurprisingly, given how major an idea this was in the history of maths.

Writing this, I’ve started wondering if all this build up could be introduced through discovery, but I think the idea is just not intuitive enough.

So then the worksheet guides the students through an investigation of some standard curves before encouraging generalisation. In my experience, it works well with a range of A-level students, and allows scope for those who work more quickly through it to generalise and prove more thoroughly.

As always, I’d love any suggestions for improvements.

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