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AP Calculus BC Flashcards: Second Derivative Test

Study Second Derivative Test in AP Calculus BC with focused flashcards that help you recognize the idea, recall the key rule, and apply it in practice-style prompts.

QUESTION

What is the second derivative of f(x)=−x4+2x2−xf(x) = -x^4 + 2x^2 - x?

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ANSWER

f′′(x)=−12x2+4f''(x) = -12x^2 + 4. Differentiate f′(x)=−4x3+4x−1f'(x) = -4x^3 + 4x - 1 to get the second derivative.

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AP Calculus BC: Analytical Applications of Differentiation

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This deck focuses on Second Derivative Test, giving you a quick way to review the definitions, rules, and examples that matter most for AP Calculus BC.

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Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Practice questions

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The function ss has a critical point at x=−2x=-2 and s′′(−2)=9s''(-2)=9; classify x=−2x=-2.
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