That isn't correct?
What about the third point? has three solutions. is also a solution.
the diagram shows the curve not going past x = 4 because it goes into an asymptote (according to the diagram at least) and the problem stated to use the diagram.
the book gives the point (2 -2sqrt5, -2sqrt(10 sqrt(5) -22) but in solving for x, I did see that x = 0 was a solution but the book didn't have that as an answer. Inputing the value of x back into the original equation as 0, it yields y= 0. the point is then (0, 0)
If you plug (0,0) into the derivative you found, you are dividing by zero. So, that was my mistake. The derivative is not defined at (0,0), so the function does not have a tangent line at that point.