1. The problem asks to redo number 7 with a table of variation and explain step by step. 2. First, identify the function from problem 7 (assuming it is $f(x)$). 3. To create a table of variation, we need to find the critical points by solving $f'(x) = 0$. 4. Calculate the derivative $f'(x)$. 5. Solve $f'(x) = 0$ to find critical points. 6. Determine the sign of $f'(x)$ on intervals defined by critical points to know where $f$ is increasing or decreasing. 7. Use this information to build the table of variation showing intervals, sign of $f'(x)$, and behavior of $f$. 8. Finally, summarize the function's increasing/decreasing behavior and local extrema from the table. Since the original function from number 7 is not provided, please provide it to proceed with the detailed solution and table of variation.