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A differential equation is a relation that involves an unknown function and its derivative. There are many kinds of differential equations and tons of specialized techniques we may use to solve them. Fortunately, on the AP Calculus exams you will only encounter a handful of the most basic kinds. Basic Differential Equations: Integration You have […]
This review article is all about optimization. Here, you’ll learn the tools and techniques for setting up and solving these often difficult problems. And along the way, we’ll work out a few examples! Optimization The method of optimization uses derivatives to find maximum or minimum values. However, the functions that need to be optimized typically […]
Calculus is primarily the study of rates of change. However, there are numerous applications of derivatives beyond just finding rates and velocities. In this review article, we will highlight the most important applications of derivatives for the AP Calculus AB/BC exams. Applications of Derivatives Here is a list of some of the essential derivative applications. […]
One of the trickiest topics on the AP Calculus AB/BC exam is the concept of inverse functions and their derivatives. In this review article, we’ll see how a powerful theorem can be used to find the derivatives of inverse functions. Then we’ll talk about the more common inverses and their derivatives. What are Inverse Functions? […]
The Shell Method is a technique for finding the volume of a solid of revolution. Just as in the Disk/Washer Method (see AP Calculus Review: Disk and Washer Methods), the exact answer results from a certain integral. In this article, we’ll review the shell method and show how it solves volume problems on the AP […]
As you prepare for the AP Calculus exam, it’s important to know what you’re getting into. Hopefully you’ve already taken a look at the list of topics, but this article is about one topic in particular: limits. Read on to familiarize yourself with the common limits that you’ll encounter on the test!
So you may have memorized all of the derivative rules. You might be able to derive f '(x) from f(x) no matter how complicated the function is. But how are you at estimating derivatives directly from the graph? As we’ll see in this review article, it’s all about slope! The Derivative Measures Slope Let’s begin with […]
Calculus is the study of motion and rates of change. In fact, Isaac Newton develop Calculus (yes, like all of it) just to help him work out the precise effects of gravity on the motion of the planets! In this short review article, we’ll talk about the concept of average rate of change. We’ll also […]
What’s a discontinuity? Any point at which a function fails to be continuous is called a discontinuity. In fact, there are various types of discontinuities, which we hope to explain in this review article. Points of Discontinuity The definition of discontinuity is very simple. A function is discontinuous at a point x = a if […]
You know you’ll have to know your derivatives inside and out in order to score high on the AP Calculus exam. But what are the most common derivatives you’ll see on the test? In this short article, we’ll let you in on the secret! Know the Basics First of all, it’s very important to have […]