The function provided in the image is:

$f(x) = 4x^4 - 12x^3 + x^2 + 12x + 4$

Would you like to analyze this function in a specific way (e.g., find its roots, critical points, or analyze its behavior)? Let me know how you'd like to proceed.

Related questions:

1. Would you like to find the derivative of $f(x)$?
2. Do you want to find the critical points of the function?
3. Are you interested in solving for $f(x) = 0$?
4. Would you like to analyze the concavity of the function?
5. Should we check for inflection points?

Tip: Always check the behavior of a polynomial function at its critical points and endpoints to understand the overall shape of the curve.