### Unit 2: Instantaneous Rate of Change: The Derivative

In this unit, you will study the instantaneous rate of change of a function. Motivated by this concept, you will develop the notion of limits, continuity, and the derivative. The limit asks the question, "What does the function do as the independent variable becomes closer and closer to a certain value?" In simpler terms, the limit is the *natural tendency* of a function. The limit is incredibly important due to its relationship to the derivative, the integral, and countless other key mathematical concepts. A strong understanding of the limit is essential to success in the field of mathematics.

A derivative is a description of how a function changes as its input varies. In the case of a straight line, this derivative, or slope, is the same at every point, which is why we can describe the slope of an entire function with one number when it is linear. You will learn that we can do the same for nonlinear functions. The slope, however, will not be constant; it will change as the independent variable changes.

**Completing this unit should take you approximately 16 hours.**