Rate of Chance in Calculus

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Rate of chance is a calculus term that typically applies to one of two things. Find out about rate of chance in calculus with help from an experienced math tutor in this free video clip.

Part of the Video Series: Calculus Explained

Video Transcript

Hi there. This is Ryan Malloy here at the Worldwide Center of Mathematics. In this video, we're going to discuss the concept of the rate of change as it applies to calculus. So when you hear the term rate of change in calculus, there's typically one of two meanings that's being talked about. Let's say we've got some function f of x, we won't define it for now. There's two things we might be asked about it. The average rate of change over an interval, which is sometimes called the AROC, or average rate of change, and we have the instantaneous rate of change at a value. Sometimes called the IROC. So how do we express the average rate of change over an interval? If we are looking at the average rate of change on the interval from a to b where a and b are simply two numbers that are within the domain of our function. The average rate of change can be expressed quite simply as value of the function at a minus the value of the function at b divided by a minus b. And it's just that simply. The instantaneous rate of change is a little bit more complicated and it uses some more advanced techniques. So let's say that we want instantaneous rate of change at some value a. This is given by a limit. The limit as h approaches zero where h is just some arbitrary variable of f of a plus h minus f of a divided by h. Over here we can't simply plug in h directly since there'll be a zero in the denominator. But typically this limit is not very difficult to compute, and as a result, there are a number of rules and properties that have been well established as to how to do it quickly. For example, if we have f of x equals let's say x cubed. Instead of computing this limit for x cubed, we can simply use what's known as the power rule. And so if we want to find the instantaneous rate of change of f of a, sometimes indicated by f prime a. Well we'd simply take three x squared at a. Which just gives us three a squared. So for example if a were two, we get two squared is four times three is 12. My name is Ryan Malloy and we've just discussed the rate of change in calculus.