Question

Hi. I am new to the forum. I'm taking Calculus 1. Just listened to first set of derivatives lectures. I vaguely remember this stuff from my engineering days (long ago), but what's really missing for me at this point is an application -- can anyone tell me a reason why we might be looking for the slope of the secant to a function? Is there a real world application for this kind of thing? Many thanks in advance.

Answer 1

The derivative gives you the instantaneous rate of change (which is the slope of the tangent line), and is used in physics, where the first derivative is the velocity and the second derivative is the acceleration.
I also think it is used in financial models and calculations, but don't know for sure, but I'm sure there are many other applications of calculus both in physics and other areas as well.

Answer 2

In the real world the rate of change of displacement gives velocity: dx/dt, rate of change of velocity gives acceleration dv/dt, from which we can calculate force, and thereby energy. The rocket flies using the concept of f proportional to dm/dt (where m is the mass of the remaining burning fuel).
For a civil engineer, suppose he want's to attach a straight pipeline to a parabolic tower, he shall need to find the slope of the parabola at that point to calculate the length of pipe reqd.
It can be used in probability to find the rate of change of your winning percentage (random variable), and who knows, you might be able to beat a casino, and become a billionaire. :)

And the list goes on... Calculus is the most important thing ever. And the most interesting too, in maths. At least till where I've studied.

Answer 3

Thank you. Very helpful examples.

Answer 4

I have just completed unit 1, I think unit 2 is about the applications of differentiation