Local Linearity and Linearization

AP Calculus AB· difficulty 3/5

Use linearization at a=4a = 4 to estimate 4.1\sqrt{4.1}.

  • A

    2.052.05

  • B

    2.0252.025

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  • C

    22

  • D

    2.12.1

Explanation

f(x)=xf(x) = \sqrt x, f(4)=2f(4) = 2, f(4)=1/4f'(4) = 1/4. L(x)=2+(1/4)(x4)L(x) = 2 + (1/4)(x-4). L(4.1)=2+0.025=2.025L(4.1) = 2 + 0.025 = 2.025.

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