The Intermediate Value Theorem is sometimes used to prove that roots exist. For example, $f ( x ) = 5 \sqrt [ 3 ] { x - 2 } - 4$ is a continuous function. Given $f(2) = −4$ and $f(3) = 1$, does $f(x)$ have a root somewhere between $x = 2$ and $x = 3$? Why or why not?