1.1 Introducing Calculus: Can Change Occur at An Instant?

In AP Calculus, limits can be used to represent a constant change in functions. The rate of change of a function is equal to the formulas ΔY/ΔX or (Y2- Y1)/(X2-X1). While this formula may look scary, it’s actually just the slope formula. You may remember this as rise over run or the change in y over the change in x. 🔺 So in short, yes, change can occur at an instant. As you get further along in the course, you’ll learn about derivatives. Derivatives depend on limits and a derivative is the rate of change of a function at an instant, what we’ll call “instantaneous rate of change.” 🔄