Understanding the Definition of a Derivative
In this video, I want to clarify the concept of the derivative of a function, and specifically, we'll analyze its geometric interpretation.
I often encounter students who know how to calculate the derivative of a function but don't understand the underlying analysis. Therefore, in this video, I'll explain in detail the geometric interpretation of the derivative, which is simply the slope of the tangent line at a given point on a curve. Because the slope of a curve isn't the same at all points, we can't calculate it using two points that are a considerable distance apart. However, we can make the distance h (the distance in x from point x to point x plus h) smaller and smaller. By making it smaller and smaller, we can find the limit of the function and thus obtain its derivative.
Professor Arturo Cardona demonstrates how to derive the derivative in terms of limits, keeping in mind that the derivative of a function is the slope of the tangent line.
In calculus, calculating the derivative of a function is very useful and has many applications to everyday life problems.