Use linear approximation, i.e. the tangent line, to approximate $\displaystyle {1.9}^{{4}}$ as follows:
Let $\displaystyle {f{{\left({x}\right)}}}={x}^{{4}}$. The equation of the tangent line to $\displaystyle {f{{\left({x}\right)}}}$ at $\displaystyle {x}={2}$ 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 $\displaystyle {1.9}^{{4}}$ is Preview Question 6 Part 3 of 3