## Calculus 8th Edition

$g'(0)$ < $0$ < $g'(4)$ < $g'(2)$ < $g'(-2)$
Explanation: $g'(x)$ corresponds to the slope of the tangent line at $(x, g(x))$ Looking at the graph you can see that $g'(0)$ is the only negative slope so it is the only value less than zero $g'(0) < 0$ Looking at relative (positive) slopes of $g'(-2)$, $g'(2)$, and $g'(4)$ you can see that $g'(-2)$ has the steepest slope, $g'(2)$ has the second highest slope, and $g'(4)$ the least out of the three. $g'(4)$ < $g'(2)$ < $g'(-2)$ Thus $g'(0)$ < $0$ < $g'(4)$ < $g'(2)$ < $g'(-2)$