Answer:
f : III
f' : II
f'' : I
Step-by-step explanation:
From x = 0 to about x = 1.5, graph III decreases; on this interval, II is negative. From x = 1.5 to x = 2, graph III increases; on this interval, II is positive. From x = 2 to about x = 2.3, graph III decreases; on this interval, II is negative. From about x = 2.3 to x = 3, graph III increases; on this interval, II is positive. And finally, from about x = 3 to about x = 4, graph III decreases; on this interval, II is negative.
Therefore, graph II corresponds with the slope trend of graph III. If III is f, II is f'.
To determine that graph I corresponds with the slope trend of graph II and is therefore f'', follow a similar process comparing graphs I and II.
If II is f', I is f''.
Therefore, f : III and f' : II and f'' : I