Chapter 4 - Applications of Derivatives
"The derivative is supremely useful because there are so many ways to think of it. It is the instantaneous rate of change, enabling us to find velocity when position is given or acceleration when velocity is given. It also described sensitivity, how change in the input variable is reflected in the change of the output variable. And it has a geometric meaning, as the slope fo the tangent to the graph of a function. In this chapter, we will explore how all of these understandings of the derivative lead to applications."
(Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. "Chapter 5." Calculus: Graphical, Numerical, Algebraic. 5th ed. N.p.: Pearson Education, n.d. 193. Print. AP Edition.)
Lesson 4.1 - Extreme Values of Functions
This lesson will teach students to find the maximum or minimum value of a function over a given interval and determine the applicability of the Extreme Value Theorem.
Lesson 4.2 - Mean Value Theorem
This lesson will teach students to apply the Mean Value Theorem to describe the behavior of a function over an interval.
Lesson 4.3 - Connecting f' and f'' with the Graph of f
This lesson will teach students to use derivatives to analyze properties of a function.
Lesson 4.4 - Modeling and Optimization
This lesson will teach students to use derivatives to solve optimization problems.
Lesson 4.5 - Linearization, Sensitivity, and Differentials
This lesson will teach students to solve problems involving the slope of the tangent line.
Lesson 4.6 - Related Rates
This lesson will teach students to solve problems involving rates of change in applied contexts.