Blog #4

Tammy Bah

2 December 2014

Applied Calculus

Blog #4

Be the Professor!

Today’s Topic: Instantaneous Rate of Change (IRC)

Opening Statement: Hey Yall! My name is Professor Tammy Bah, but rather be called Tammy and today I will be teaching how to find and calculate the Instantaneous Rate of Change (IRC) as this is vital for any student who wants to take Pre-calculus, Calculus and Applied Calculus and moving on to more developed Mathematics and Economics courses.

Lecture: I would like you to look at whatever source you want to come up with different definitions for the Instantaneous Rate of Change (IRC). Then, I would like you to find examples of things that you can find the slope of! Now, The definition of the IRC is a term that measures the rate of rate, better known as the “slope” of a curve, or better wise known as the slope of a tangent line at one given or one specific moment. The IRC is also the same as the value/number of a derivative at that certain point. To make sure that everyone understands; the slope of the tangent line is the derivative, so by calculating the IRC, we are also calculating the derivative at a specific point. The derivative measures the IRC of a function.

Terms to Know:

Tangent Line: a line that intersects a graph at one point

Slope, m as the change in y/the change in x =Δy/ Δx

Ways of Solving: There are many different ways to calculate the IRC, however for this lesson plan I will be teaching you how to find the IRC of f at the point x.

For my sample problem, attached with a picture, I will be using this formula (notion of using limits of the difference quotient to calculate the average rate of change over an interval):

IRC: 

* I will also show the IRC graphically!

Answer: The derivative of 5x-2 at any point 5 is the IRC. 

Purpose: The purpose of learning this or why we find the slope of a line is to tell you how fast a relationship between two variables at a certain point. It is important to notice that when it comes to little periods of time, the average rate of change is supposed to be equal to the IRC. Additionally, IRC is a way to show rates of change as well. The purpose of this lesson is also to allow students to find the derivative by using the concepts of limits.

Conclusion: I hope everyone had a good time getting to learn about the Instantaneous Rate of Change (IRC) and that you feel comfortable teaching it to a friend or a classmate! Have a great rest of the day :)