Unit 5: First Derivative Diagnostic

Students use derivatives to analyze the behavior of functions, including finding extrema, determining concavity, and sketching accurate graphs. This unit also covers optimization problems. Unit 5: First Derivative Diagnostic turns that idea into something you can manipulate directly and watch respond.

Students use derivatives to analyze the behavior of functions, including finding extrema, determining concavity, and sketching accurate graphs. This unit also covers optimization problems. It focuses on Mean Value Theorem (MVT), Extreme Value Theorem (EVT), First Derivative Test (Increasing/Decreasing), Second Derivative Test (Concavity), Points of Inflection, Optimization Problems from the “Unit 5: Analytical Applications of Differentiation” section.

AP Calculus AB is a college-level course that explores the concepts of limits, derivatives, and integrals. Students learn to approach mathematical problems through multiple representations—graphical, numerical, analytic… This demo is the interactive piece for the “Unit 5: Analytical Applications of Differentiation” section. Open the full AP Calculus AB course wiki at https://www.getlykke.com/explore/public/ap-calculus-ab-c14bedc7-55ee-4bd3-99ff-a9a537a06a66 for notes, flashcards, quizzes and the other demos.

You'll build intuition for Mean Value Theorem (MVT), Extreme Value Theorem (EVT), First Derivative Test (Increasing/Decreasing), Second Derivative Test (Concavity), Points of Inflection, Optimization Problems — and, crucially, see how they behave when you change the inputs, which is hard to get from a textbook or lecture on AP Calculus AB alone.