Intuitive Approach to Derivatives

This lecture aims to provide a better intuition on the concept of derivatives, using the example of a cyclist going up and down a hill to explain how the derivative represents speed variations. By subdividing the journey into multiple intervals, the notion of average speed is refined into instantaneous speed, leading to the definition of derivatives. Graphically, the derivative represents the slope of a tangent line to the function, allowing for a more accurate representation of speed variations. Understanding this concept graphically enables the reconstruction of the speed graph based on the position graph, emphasizing the relationship between slopes and speeds. By starting from basic physical notions and using intuition, the lecture guides the audience through the mathematical definition and graphical representation of derivatives.