Find the values of $\displaystyle {x}$ where the tangent line to the graph of $\displaystyle {f{{\left({x}\right)}}}=\frac{{1}}{{x}}$ is parallel to the line $\displaystyle {y}=-{5}{x}+{9}$.

Give exact answers (not decimal approximations).

(Tip: To enter $\displaystyle \sqrt{{{a}}}$, type either sqrt(a) or a^(1/2).)

The greater solution is x = Preview Question 6 Part 1 of 2  
and lesser solution is x = Preview Question 6 Part 2 of 2