Differentiation and Tangent to a curve

A file to show students how the gradient function of a curve x, is the value of the gradient of the tangent to the curve, at a corresponding value of x. I would start by sliding the "dy/dx against x" graph down, to hide it, so can initially focus on and emphasise the gradient of a curve, and how this value is changing for different x values. Students can then be asked to look at how m changes. If we drew a graph of m, what would we expect it to look like? The value of m is then traced on the graph below as the slider a is moved. The slide can be stopped at values of a of interest, e.g. stationary points etc. If you want to cancel the trace, just move the graph below with the curser slightly, and it will disappear. Appropriate for: L2 Further maths : Alevel maths