Taylor Series

Local Linear Approximation


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

Estimate the value of 0.9793\sqrt[3]{0.979} using local linear approximation for the function f(x)=1+x3.f(x)=\sqrt[3]{1+x}.

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

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

What is the local linear approximation of the function f(x)=14x35xf(x)=14x^3-5x near x=1?x = 1?


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