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