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Local Linearity and Linearization

AP Calculus AB· difficulty 3/5

Use linearization to estimate 27.63\sqrt[3]{27.6} near a=27a = 27.

  • A

    3.0223.022

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  • B

    3.0333.033

  • C

    3.063.06

  • D

    3.0113.011

Explanation

f(x)=x1/3f(x) = x^{1/3}, f(27)=3f(27) = 3, f′(27)=(1/3)(27)−2/3=1/27f'(27) = (1/3)(27)^{-2/3} = 1/27. L(27.6)=3+(1/27)(0.6)=3+0.0222≈3.022L(27.6) = 3 + (1/27)(0.6) = 3 + 0.0222 \approx 3.022.

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