Lesson 2: 4.2 The Mean Value Theorem
Duration of Days: 2
Lesson Objective
- Determine whether a function is both continuous and differentiable over a fixed interval
- Determine the average slope (mean value) of the function over that fixed interval
- Determine where the slope of the function is equal to the average slope
- Is the function both continuous and differentiable over the interval?
- What is the average slope of the function over that interval?
- Where is the slope of the function (derivative) equal to the average slope over that interval?
- What is the average revenue for a business over a specified interval of time?
- Rolle's Theorem
- Mean Value Theorem
(Continuity, Differentiability, Derivatives)
Average slope of a continuous and differentiable function over a fixed interval.
DOK levels 1-4
Average output/revenue for a business over time, etc.
Students will sometimes forget to check the assumptions of the theorems before determining the average slope (mean value).
Students may stop after finding one value that satisfies the Mean Value Theorem when there may be multiple.
Homogeneous grouping and whole class discussion.
Section assessment
Problems assigned from book, specific business revenue data