AP Calculus AB FRQ #4 Explained: 2012 Exam (Non-Calculator)

Step-by-step solution to Free Response Question #4 from the 2012 AP Calculus AB exam (non-calculator).

This problem combines procedural calculus skills and conceptual reasoning, including finding derivatives, writing equations of tangent lines, evaluating integrals using substitution, and applying the formal definition of continuity.

In this video, I show how to structure your work clearly, justify each step, and apply exam-appropriate reasoning to earn full credit on the AP Calculus AB free response section.

Ideal for students preparing for the AP exam or reviewing key calculus concepts in context.

Watch the full playlists for the 2012 Exam here:
MCQs —    • 2012 AP Calculus AB – Multiple Choice Ques...  
FRQs —    • 2012 AP Calculus AB – Free Response Questi...  

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0:00 Problem overview
0:34 Part (a) — Calculate a derivative f'(x)
3:33 Part (b) — Find the equation of a tangent line
6:02 Part (c) — Use the formal definition of continuity
11:23 Part (d) — Use integration by substitution
16:40 Next steps