Calculus For Beginners - Why Do We Need Derivatives ? (Part 1)

Calculus For Beginners-The Basics Of Derivatives

Video Outline

Brief Outline:
Why derivatives are so important in mathematics (Calculus)?
Are Derivatives related to tangents?

To make the students understand real life scenarios are changed in to Mathematics with the help of functions. Functions are changed in to graphical format to observe the increase, decrease, maximum/minimum points etc. But plotting a graph is not always feasible so we take the help of Slope of the tangent of the functions at various points and learn that Slope of tangents can be used as an indicator of increase, decrease, maximum/minimum points. The video concludes by claiming that the Slope of a tangent to a function at any point is nothing but the derivative of the function.

Detailed Outline :

Why derivatives are so important in mathematics (Calculus)?
Are Derivatives related to tangents?

Consider a function y = f(x). Now imagine its graph. The evaluation of slope of tangent to the graph is an important task in Mathematics.

I will tell you why?

If you imagine a parabola or sin x or cos x, then you will notice that we can make tangents at each and every point. You will notice one more thing….the slope of tangents drawn and any point on the graph where the graph is increasing will be positive and the slope of tangents drawn at decreasing points will be negative and at maximum and minimum points the tangents are parallel to the x axis and hence the slope will be zero.

My point is ‘slope of tangent to a graph’ is an excellent indicator for the nature of the graph.

Now in the 1600s the forefathers of Calculus, Sir. Issac Newton and Leibniz has gifted us with one of the most powerful tool for this task. And that tool is the derivative of a function.

The reason I claim derivatives to be powerful is because the derivatives themselves are functions and hence it gives the slope of the tangent not only at one point but at any desired points.

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Video Objectives

This video is an introduction to Derivatives