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Taylor Series

Local Linear Approximation

If $f(1)=4$ and $f'(1)=6,$ which of the following is the best local linear approximation for $f(1.01)?$

4.60 4.30 7.00 4.06

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Estimate the value of $\sqrt[3]{0.979}$ using local linear approximation for the function $f(x)=\sqrt[3]{1+x}.$

0.972 0.986 0.993 0.965

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Use differentiation to estimate the value of $\sqrt{16.5}$ .

4.062 4.124 4.186 4.248

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Estimate the value of $\displaystyle \frac{6}{(1-x)^2}$ at $x=0.02$ using local linear approximation.

6.48 6.60 6.24 6.12

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What is the local linear approximation of the function $f(x)=14x^3-5x$ near $x = 1?$

{42}x^2-5

{42}x^2+5

{37}x-28

{37}x+28

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