Answer: Provided the function, we have to answer the questions (a) to (f), the function is as follows:

(a) The first derivative of (1) is as follows:

(b) The second derivative is calculated using the same method as in part (a), only the difference is that it is calculated twice:

(c) The interval where the function is increasing can be found by inspecting the graph of the original function or the equation (1):
The plot is as follows:
The interval on which the function is increasing is:
![x=[-\infty,-7]\text{ and }x=[5,\infty]](https://img.qammunity.org/2023/formulas/mathematics/college/kh98iu0nrg2yx0g4sy4pcb8li9bfuimq0t.png)
(d) Similarly, the decreasing interval is as follows:
![x=[-7,5]](https://img.qammunity.org/2023/formulas/mathematics/college/xvg6ep5cwomqj3pev93pt83i76y608b3o4.png)
(e) Concave upward:
![x=[-7,+\infty]](https://img.qammunity.org/2023/formulas/mathematics/college/lj20zf4expqt71o3zku8tkyg47jmaa0gss.png)
(f) Concave downward:
Similarly, the concave downward is on the following interval:
![x=[-\infty,-7]](https://img.qammunity.org/2023/formulas/mathematics/college/x5791brwhprnqtcep0bg7c6td25ov84mth.png)