Polynomials and Other Functions
A Look Ahead to Calculus
In each math class that we take, we absorb and learn tons of information and ideas. But sadly, some of these ideas and concepts are sometimes lost or forgotten as we progress to our next course.
So let’s Look Ahead to Calculus and see how Polynomials and Other Functions help us to connect the dots from one class to the next.
Again, it is my desire that we can connect our current knowledge with what we will be seeing in the future, in hopes that we will see how math is all connected and give you the best foundation for when you see these exact same concepts again in calculus!
We will begin with an understanding of the similarities and differences between an Open Interval and a Closed Interval, and how they impact turning points in a graph.
Turning points, as you remember, are where we can identify maximum and minimum values, as Cool Math nicely states. But, in this lesson we’re going to dig deeper and look at graphs and learn how to spot Local (Relative) Maximums and Minimums but also Absolute (Global) Maximums and Minimums as well.
Then we will discuss the importance of the Extreme Value Theorem, and how it helps us to determine whether or not we will have Extrema in our graph.
Additionally, we will formalize definitions and notations so we can properly identify Increasing and Decreasing Intervals by investigating the slope of a graph. And this will help us to segue into how we can formally identify Maximums or Minimums (i.e., slope of zero or undefined).
Likewise, we will also look at how to spot Inflection points and Concavity Intervals.
All of the concepts that we are going to discuss during this lesson are foundational in your understanding of applications of derivatives for calculus.
But, what’s so great is that you already know it all, we just need to cement it into your brain!
Polynomial Functions in Calculus – Video
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