One of the main difficulties
students encounter when beginning to study the derivative of a
function is understanding it in geometrical terms. Whereas calculating
derivatives is usually fairly straightforward and can even be quite
appealing, applying the geometric interpretation of a derivative at a
point becomes a more complex problem. This is often due to not having
a clear understanding of the concept, rather than the problem itself
being too complex.
The activities which
follow are designed to familiarise the student with the concepts of
the secant and tangent to a curve, to observe how the former
approaches the latter and to understand the limit as a process which
can be observed and checked.
