Tangent Line

In differential calculus, understanding how a quantity changes at an exact point is central to interpreting dynamic systems. This can be illustrated by analyzing a car traveling along a winding road. The car’s trajectory is represented as a continuous curve, and the direction in which it moves at any instant is given by the tangent to that curve...

Imagine a car traveling on a winding road; its position over time can be represented as a smooth curve on a graph.

To observe the change in the car's position between two points, a straight line can be drawn connecting them - this line is called a secant line.

The slope of the secant line captures the car’s average velocity during th...