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Local Linearity and Linearization

AP Calculus AB· difficulty 3/5

x (a, f(a))

The dashed tangent line at x=ax=a gives the linearization L(x)=L(x) =:

  • A

    f′(a)(x−a)f'(a)(x-a)

  • B

    f(a)+f′(a)(x−a)f(a) + f'(a)(x-a)

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  • C

    f(x)−f(a)f(x) - f(a)

  • D

    f(a)⋅xf(a) \cdot x

Explanation

The linearization is L(x)=f(a)+f′(a)(x−a)L(x) = f(a) + f'(a)(x - a).

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