Calculus Unit 6

Big Idea:

Derivatives

Student Expectations:

Focus Standards

EU 2.2: A function’s derivative, which itself a function, can be used to understand the behavior of the function.

• EK 2.2A1: First and second derivatives of a function can provide information about the function and its graph including intervals of increase or decrease, local (relative) and global (absolute) extrema, intervals of upward or downward concavity, and points of inflection.
• EK 2.2A2: Key features of functions and their derivatives can be identified and related to their graphical, numerical, and analytical representations.
• EK 2.2A3: Key features of the graphs of , , and are related to one another

EU 2.3: The derivative has multiple interpretations and applications including those that involve instantaneous rates of change.

• EK 2.3C3: The derivative can be used to solve optimization problems, that is, finding a maximum or minimum value of a function over a given interval.

EU 2.4: The Mean Value Theorem connects the behavior of a differentiable function over an interval to the behavior of the derivative of that function at a particular point in the interval.

• EK 2.4A1: If a function is continuous over the interval and differentiable over the interval , the Mean Value Theorem guarantees a point within the open interval where the instantaneous rate of change equals the average rate of change over the interval.

Student Learning Targets:

• I will use derivatives to analyze properties of functions
• I will solve problems involving optimization
• I will use the first and second derivative tests
• I will understand and apply the Mean Value and Rolle’s Theorems

Essential Questions:

Extra Information:

Adopted Textbook:

District Grading Policy

Texas Gateway Online Resource Center