Suppose $\displaystyle$ is a continuous function where $\displaystyle {f{{\left({7}\right)}}}={6}$ and $\displaystyle {f}'{\left({7}\right)}={5}$.

The equation of the line tangent to the graph of $\displaystyle {y}={f{{\left({x}\right)}}}$ at $\displaystyle {x}={7}$ will be $\displaystyle {y}=$Preview Question 6 Part 1 of 4  

So $\displaystyle {f{{\left({x}\right)}}}\approx$Preview Question 6 Part 2 of 4   for $\displaystyle {x}$ close to $\displaystyle {x}={7}$.

Based on this, $\displaystyle {f{{\left({7.9}\right)}}}\approx$ Preview Question 6 Part 3 of 4  

A solution to $\displaystyle {f{{\left({x}\right)}}}={0}$ is $\displaystyle {x}\approx$Preview Question 6 Part 4 of 4