Lectures>Practice

# Rate of Change

We talked about the derivative as the rate of change of a function back when we first deriving it. At the time, we were just talking about arbitrary functions so the discussion was very abstract. Now we're going to make this practical by looking at specific functions like ones describing the speed and position of an object.

# Videos

In the first derivative lectures, I talked about the derivative being another way of saying "the rate of change". In this lecture, we'll see how this can be applied to concepts taken from the physics of moving objects.
How much will it cost you to produce one more item? How much profit will you get from selling one more? This idea of the value of the next item in a process is what's called the "marginal change". In this lecture, we'll see how this value can be approximated using the derivative of the corresponding value function.
Suppose you decide to increase the cost of your product by \$1. What affect will that have on the product's demand? Will your customers be willing to pay a little more or is that going to make a dramatic change in your sales. We can use differentiation to describe this property that economists call elasticity.