Writing Justifications for AP Free-Response Questions
Learn how to write clear, mathematically correct justifications for AP Calculus free-response questions, including theorems, conclusions, evidence, and common mistakes.
Using the Second Derivative to Determine Concavity
Learn how to use the second derivative to determine where a function is concave up or concave down, with step-by-step AP Calculus examples and practice problems.
Using the First Derivative to Determine Increasing and Decreasing Intervals
Learn how to use the first derivative and a sign chart to determine where a function is increasing and decreasing, with fully worked AP Calculus examples.
Using Sign Charts to Analyze Function Behavior
How to use sign charts to analyze increasing and decreasing behavior, critical points, local extrema, and concavity in AP Calculus AB & BC.
The Second Derivative Test for Local Extrema
Learn how to use the second derivative test to determine whether a critical point is a local maximum or minimum, with step-by-step AP Calculus examples and practice problems.
The Mean Value Theorem Explained
Understand the Mean Value Theorem, how to verify its conditions, find guaranteed points, and interpret what it means for AP Calculus AB & BC.
The First Derivative Test for Local Extrema
Learn how to use the First Derivative Test to determine local maxima and minima, with a step-by-step method and fully worked AP Calculus examples.
Solving Optimization Problems: An Introduction
Learn how to set up and solve optimization problems in AP Calculus using derivatives, constraints, critical points, and endpoint checks.
Sketching Graphs of Functions from Derivative Information
Learn how to sketch the graph of a function from information about its first and second derivatives, including increasing/decreasing intervals, extrema, concavity, inflection points, and critical points.
Second Derivative Applications: Jerk and Concavity in Motion
Understand how the second derivative describes acceleration and concavity in motion, and how the third derivative describes jerk, with fully worked AP Calculus examples.