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The function provided is:

\[
f(x) = \frac{3x^3 + x + 2}{5x^2 + 1}
\]

Would you like to:
1. Find the derivative of this function, \( f'(x) \)?
2. Determine the critical points by setting \( f'(x) = 0 \)?
3. Analyze the behavior of the function as \( x \to \infty \) (find limits)?
4. Evaluate \( f(x) \) at specific values of \( x \)?
5. Determine the asymptotes of the function?

Let me know if you'd like any of these details or something else.

**Tip:** When differentiating rational functions, the quotient rule is essential!

Learn how to differentiate and analyze the rational function f(x) = (3x^3 + x + 2) / (5x^2 + 1) using the quotient rule. This includes finding the derivative, determining critical points, and evaluating limits as x approaches infinity. Perfect for calculus students.

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