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AP Calculus BC Flashcards: Local Linearity And Linearization

Study Local Linearity And Linearization 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

Evaluate L(x)L(x) for f(x)=cos(x)f(x) = \text{cos}(x) at x=π2x = \frac{\text{π}}{2} using x=π2+0.1x = \frac{\text{π}}{2} + 0.1.

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ANSWER

L(x)=0−0.1=−0.1L(x) = 0 - 0.1 = -0.1. f(π2)=0f(\frac{\pi}{2}) = 0, f′(π2)=−1f'(\frac{\pi}{2}) = -1, so slope is negative.

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AP Calculus BC: Contextual Applications of Differentiation

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This deck focuses on Local Linearity And Linearization, 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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A temperature model TT satisfies T(10)=68T(10)=68 and T′(10)=1.5T'(10)=1.5. What is the linear approximation near t=10t=10?
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