Answer
$(5.065, +\infty)$
Work Step by Step
To solve the given inequality graphically, do the following steps:
(1) Use a graphing utility to graph $y=x^3-4x^2-5x$ (refer to the red graph) and $y=2$ (refer to the blue graph);
(2) Identify the points where the graphs intersect each other.
The graphs intersect at $x=5.065$.
(3) Identify which region/s satisfy the given inequality.
Notice that when $x>5.065$, the graph of $y=x^3-4x^2-5$ (the red graph) is above the graph $y=2$ (the blue graph). Above means that the value of the function is greater than the other.
The inequality involves greater than so $5.065$ is not included in the solution.
Thus, the solution to the given inequality is:
$(5.065, +\infty)$
(refer to the attached image below for the graph)
