https://file.aiquickdraw.com/mathbot/file/1726954531593ma2pi06p.jpg

The function depicted in the image is:

\[
f_4(x, y) = \frac{x^2 y}{x^2 - y}
\]

Would you like to explore the behavior of this function (such as finding critical points, limits, or partial derivatives)? Feel free to ask for details.

Here are five related questions you might find useful:
1. How do you compute the partial derivatives of \( f_4(x, y) \) with respect to \(x\) and \(y\)?
2. What are the critical points of \( f_4(x, y) \)?
3. Can the function \( f_4(x, y) \) have asymptotes, and how would you determine them?
4. How would you graph the function \( f_4(x, y) \) in three dimensions?
5. What are the conditions under which \( f_4(x, y) \) is undefined?

**Tip:** When dealing with rational functions like this, identifying when the denominator becomes zero is crucial for understanding discontinuities or undefined regions.

What is the function f_4(x, y) and how does it behave?

Learn how to analyze the function f_4(x, y) = x^2 y / (x^2 - y). This problem covers key concepts in multivariable calculus, including critical points, limits, and identifying discontinuities in rational functions.

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