The function you provided is:

\[
f(x) = x + \frac{36}{x}
\]

Would you like to find the derivative, analyze properties of this function, or something else?

Here are some related questions that might help:
1. What is the derivative of \( f(x) = x + \frac{36}{x} \)?
2. How do we find the critical points for \( f(x) = x + \frac{36}{x} \)?
3. What is the behavior of \( f(x) \) as \( x \) approaches zero or infinity?
4. Can we determine the points of local minima or maxima for \( f(x) \)?
5. How can we plot the function \( f(x) = x + \frac{36}{x} \) for different values of \( x \)?

**Tip:** When dealing with rational functions like \( f(x) = x + \frac{36}{x} \), consider both the derivative for critical points and the limit behavior at points where the function is undefined (like \( x = 0 \)).

Explore the function f(x) = x + 36/x with step-by-step guidance on finding its derivative, critical points, and understanding its behavior at infinity and near zero. Perfect for high school calculus students and early college learners looking to understand rational functions and optimization techniques.

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