Answer:
g'(0) < 0 < g(4) < g(2) < g(-2)
Step-by-step explanation:
You get started by reading the question and understanding what it is asking. Here, it wants to know what the relative signs and magnitudes of the slopes are at different points on the curve.
If the curve goes up to the right, the slope (g') is positive. So, the signs of the slopes at -2, 0, 2 and 4 are +, -, +, +, respectively. That tells you right away that ...
g'(0) < 0
Now, you have to decide which point on the curve has the highest slope. It is fairly easy to see that the slope at x=4 is less than either of the slopes at x=2 or x=-2. The trick is to decide whether the curve is steeper at -2 or at +2.
My call is that g(-2) > g(2) > g(4), so the increasing order is ...
g'(0) < 0 < g(4) < g(2) < g(-2)
