Students confuse the two Mean Value Theorems - the Mean Value Theorem for Derivatives and the Mean Value Theorem for Integrals. Comparing them side by side reinforces that one deals with slope and one deals with net area, Algebra I vs Geometry. In this foldable the students list the conditions needed to apply the theorems and the symbolic theorems, discuss the geometric interpretations of the theorems, and work examples symbolically, with tabular function, and graphically.
My students encounter this concept in the Larsen Calculus textbook in Ch. 4 on Integration after they learn simple antiderivatives, definite integrals Riemann and trapezoidal sums, integration strategies and the Fundamental Theorems of Calculus thus the numbering 4-5. The examples do not involve the transcendental functions which are introduced in a later chapter in Larson Calculus.
This foldable is formatted so that it can be used alone or glued into an Interactive Notebook. Hope this is helpful. Enjoy!
Other foldables related to the Integration chapter:
Calculus Foldable 4-1: Simple Antiderivative Rules
Calculus Foldable 4-2: Integral as Area
Calculus Foldable 4-3: Integration Strategies
Calculus Foldable 4-4: Fundamental Theorems of Calculus
Table of Contents for the Integration chapter:
Calculus Interactive Notebook 4: Integration