Geometric interpretation of the derivative

Tangent to a curve at a point

Derivative of a function at a point

One of the greatest difficulties which pupils who start to study the derivative of a function have is the understanding of its geometrical meaning.  While they usually find the calculation of derivatives easy and even appealing, the application of the geometrical interpretation of the derivative at a point becomes a complex problem, although it shouldn´t be, because of the fact that in many cases they have not managed to acquire the concept clearly.      

The activities on these pages intend that the pupil familiarises with the concepts of secant and tangent to a curve, observes how the approximation is produced and understands the limit as a process which can be seen and verified. 

	Ministerio de Educación, Cultura y Deporte. Año 2000