Chapter 3 - The Derivative In Graphing And Applications - 3.1 Analysis Of Functions I: Increase, Decrease, and Concavity - Exercises Set 3.1 - Page 195: 8

So we need to show the signs of f' and f'' in the following intervals (1, 2), (2, 3), (3, 4), (4, 5), (5, 6), and (6, 7),which is referring to the graph in Q.7 In the interval (1,2), the function is decreasing. Therefore f' would have a negative sign. The concavity is up, therefore f'' has positive sign. In the interval (2,3),the function is decreasing therefore the f' would have negative sign. While the concavity is down therefore f'' would have negative sign. In the interval (2,3) the function is decreasing therefore the f' would have negative sign. While the concavity is down therefore f'' would have negative sign. In the interval (3,4) the function is decreasing therefore the f' would have negative sign. While the concavity is up therefore f'' would have positive sign. In the interval (4,5) the function is increasing therefore the f' would have positive sign. While the concavity is up therefore f'' would have positive sign. In the interval (5,6) the function is increasing therefore the f' would have positive sign. While the concavity is down therefore f'' would have negative sign. In the interval (6,7) the function is decreasing therefore the f' would have negative sign. While the concavity is down therefore f'' would have negative sign.

Step by Step explaination is not need since we only need to observe the graph here.