Limit, Continuity and Differentiability: JEE Main 2025 Mathematics question

Let $f: \mathbb{R} \to \mathbb{R}$ be a polynomial function of degree four having extreme values at $x = 4$ and $x = 5$. If $\displaystyle \lim_{x \to 0} \frac{f(x)}{x^2} = 5$, then $f(2)$ is equal to: