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Gradients of tangents

Aim: Explore the gradient of a chord or secant and generalise. Visually see the gradient of the tangent as the limiting value as the two points get closer together.
Apps: InteractiveDiffCalc, Main
InteractiveDiffCalc is an application that was added in version 3 of the Classpad operating system. The strength in the InteractiveDiffcalc app is being able to follow the first principles approach visually. By dynamically moving the points closer together students can see the secant getting closer to the tangent.
It also supports the development of the idea of the gradient function and taking time to understand the plotting of the gradient at specific points is a neat way of encouraging students to develop this concept.

I would use this to introduce differential calculus at Year 11 or as a refresher in Year 12.

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