Calculus AB - Unit Two
Using derivatives to describe the rate of change of one variable with respect to another variable allows students to understand change in a variety of contexts. In AP Calculus, students build the derivative using the concept of limits and use the derivative primarily to compute the instantaneous rate of change of a function. Applications of the derivative include finding the slope of a tangent line to a graph at a point, analyzing the graph of a function (for example, determining whether a function is increasing or decreasing and finding concavity and extreme values), and solving problems involving rectilinear motion. Students should be able to use different definitions of the derivative, estimate derivatives from tables and graphs, and apply various derivative rules and properties. In addition, students should be able to solve separable differential equations, understand and be able to apply the Mean Value Theorem, and be familiar with a variety of real-world applications, including related rates, optimization, and growth and decay models.
Click on a link to jump ahead to the following sections:
- Unit 1: Introduction to Derivatives
- Unit 2: The Basics of Differentiation
- Unit 3: Applying derivatives to analyze functions
- Assessment Tasks
Resources - Derivatives
The following are links to resources for Derivatives:
The following are other free resources:
- GeoGebra - Free online math tools
- Desmos - Free online graphing calculator
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