For the graph of $$ \mathrm{y}=\mathrm{f}(\mathrm{x}) $$ shown to the right, find the absolute minimum and the absolute maximum over the interval $$ [1,13] $$. Identify the absolute minimum. Select the correct choice below fill in any answer boxes within your choice. A. The absolute minimum is $$ \square $$ at $$ x= $$ $$ \square $$ and $$ x= $$ $$ \square $$ $$ \square $$. (Round to the nearest integer as needed. Use ascending order.) B. The absolute minimum is $$ \square $$ 6. $$ \square $$ (Round to the nearest integer as needed.) C. There is no absolute minimum.

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To find the absolute minimum and maximum of the function $$ y = f(x) $$ over the interval $$ [1, 13] $$, we need to evaluate the function at the endpoints of the interval and any critical points within the interval.

1. **Evaluate at the endpoints**:
   - Calculate $$ f(1) $$ and $$ f(13) $$.

2. **Find critical points**:
   - Determine where the derivative $$ f'(x) = 0 $$ or is undefined within the interval $$ (1, 13) $$.
   - Evaluate $$ f(x) $$ at these critical points.

3. **Compare values**:
   - Compare the values of $$ f(x) $$ at the endpoints and the critical points to find the absolute minimum and maximum.

Since I don't have the graph of $$ f(x) $$ to analyze, I can't provide specific values. However, you can follow these steps to find the absolute minimum and maximum:

- If you find that the minimum value occurs at $$ x = a $$ and $$ x = b $$ with $$ f(a) = f(b) $$, you would select option A.
- If the minimum value is a single number, you would select option B.
- If the function does not have a minimum value in the interval, you would select option C.

Please provide the values of $$ f(1) $$, $$ f(13) $$, and any critical points you find, and I can help you determine the correct answer.Please provide the values of $$ f(1) $$, $$ f(13) $$, and any critical points to determine the absolute minimum and maximum.

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