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Local Linearity and Linearization

AP Calculus AB· difficulty 4/5

Use the tangent at x=4x=4 to approximate 4.1\sqrt{4.1}.

  • A

    2.01252.0125

  • B

    2.12.1

  • C

    2.052.05

  • D

    2.0252.025

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Explanation

f(x)=xf(x)=\sqrt x, f′(x)=1/(2x)f'(x)=1/(2\sqrt x). At x=4x=4: f=2,f′=1/4f=2,f'=1/4. L(x)=2+(1/4)(x−4)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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