Description/Aim

This activity gives the students the opportunity to get to grips with limits and what the gradient function is. They explore the gradients of decreasing small secants using Autograph and come up with patterns for the gradients of curves in the form

y =

Why we like this activity ….

This is a great activity to get the students thinking about limits and visualising how gradients of secants approximate the gradient of curves. Formal coverage of 1st principles follows easily thereafter.

How this activity be used ….

Students need access to the software Autograph (a 30 trial can be downloaded from here)

The software is very simple and intuitive and a screencast demonstration is available.

What to expect when using this activity – from our experience

The students grasp very quickly that the shorter the secant the better the approximation to the gradient of the curve at that point

Extra Notes