Use linear approximation, i.e. the tangent line, to approximate $\displaystyle {\sqrt[{{3}}]{{{8.1}}}}$ as follows:
Let $\displaystyle {f{{\left({x}\right)}}}={\sqrt[{{3}}]{{{x}}}}$. The equation of the tangent line to $\displaystyle {f{{\left({x}\right)}}}$ at $\displaystyle {x}={8}$ can be written in the form $\displaystyle {y}={m}{x}+{b}$

where $\displaystyle {m}$ is: Preview Question 6 Part 1 of 3  
and where $\displaystyle {b}$ is: Preview Question 6 Part 2 of 3  

Using this, we find our approximation for $\displaystyle {\sqrt[{{3}}]{{{8.1}}}}$ is Preview Question 6 Part 3 of 3