2026 AP Calculus AB FRQ #6 Answers

In this video, I solve Question #6 from the 2026 AP Calculus AB Free-Response Exam — the classic "table problem"! This NO CALCULATOR question is the final FRQ of the exam and tests a ton of essential calculus skills using only values from a table.📝 What's Covered:Part A: Evaluating a Limit

Why we can use direct substitution (continuity!)
Applying the quotient property of limits
Final answer: 3/2
Part B: Chain Rule with g(x) = f(f(x))

Setting up g'(x) = f'(f(x)) times f'(x)
Carefully reading values from the table
Final answer: g'(2) = 36
Part C: FTC + u-Substitution

Using h(2) = h(0) + integral of h'(x)
u-substitution with u = 3x (don't forget the 1/3!)
Applying the Fundamental Theorem of Calculus
Final answer: h(2) = 12
Part D: FTC and Product Rule

(i) Using the FTC to find k'(x) = x² f(x)
(ii) Applying the product rule to find k''(3)
Final answer: k''(3) = 129
🎯 Topics & Skills Tested:
✅ Limits and continuity
✅ The Chain Rule (composition of functions)
✅ The Fundamental Theorem of Calculus (BOTH parts!)
✅ u-Substitution
✅ Product Rule
✅ Reading values from a table
✅ NO CALCULATOR techniques💡 Perfect For:

AP Calc AB students prepping for the exam
Anyone who struggles with table-based problems
Reviewing the Chain Rule and FTC
Teachers looking for clean FRQ walkthroughs
Students who want a quick last-minute review

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