Answer
$g'(0)\lt 0\lt g'(4) \lt g'(2) \lt g'(-2)$
Work Step by Step
Step 1. As the derivative represents the slope of a tangent line, $g'(-2)$ is the slope of the tangent line at $x=-2$, thus $g'(-2)\approx2$
Step 2. Similarly, $g'(0)\approx -1$
Step 3. We can also estimate $g'(2)\approx1$ and $g'(4)\approx0.5$
Step 4. We can arrange the numbers in increasing order as $g'(0)\lt 0\lt g'(4) \lt g'(2) \lt g'(-2)$
