The equation written in the image is:

$f(x, y, z) = x^2y + y^2z + z^2x$

This is a multivariable polynomial function of three variables, $x$, $y$, and $z$.

Would you like to see more details or have any further questions about this equation?

Here are five related questions you might find useful:

1. How do you find the partial derivatives of the function $f(x, y, z)$?
2. What are the critical points of the function $f(x, y, z)$?
3. How can you use this function in optimization problems?
4. What are some applications of functions involving multiple variables like this?
5. How do you compute the gradient of a multivariable function?

Tip: When working with multivariable functions, remember that the behavior of the function can depend on the relationship between the variables.