https://file.aiquickdraw.com/mathbot/file/1727591235827wo8sca62.jpg

The OCR text extraction was incomplete, but from the visible part of the image, the problem is to find \( f''(3) \) given the function:

\[
f(x) = \frac{x^2}{3 + x}
\]

Let's proceed by finding the second derivative \( f''(x) \), and then evaluate it at \( x = 3 \).

### Steps:
1. First, find \( f'(x) \) using the quotient rule:
   \[
   f'(x) = \frac{(3 + x) \cdot 2x - x^2 \cdot 1}{(3 + x)^2}
   \]

2. Then, find \( f''(x) \) by differentiating \( f'(x) \).

3. Finally, evaluate \( f''(3) \).

I will begin the calculations now.The second derivative of the function \( f(x) = \frac{x^2}{3 + x} \), evaluated at \( x = 3 \), is:

\[
f''(3) = \frac{1}{12}
\]

Let me know if you need further clarification or details!

Here are 5 related questions you might find useful:
1. How do you apply the quotient rule for differentiation?
2. What are common errors to avoid when differentiating complex fractions?
3. How do you find the second derivative of a rational function?
4. Can the second derivative always be interpreted as concavity?
5. How do you use symbolic computation tools for differentiation?

**Tip**: Always simplify your expressions step by step to avoid errors in longer calculations.

This detailed solution walks through finding the second derivative of the function f(x) = x^2 / (3 + x) and evaluates it at x = 3. It covers key calculus concepts such as the quotient rule and differentiation of rational functions. Ideal for advanced high school or early university students.

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