UGAT Bangalore: CalculusApplication of Derivatives. Free, no login required.

Let $f: \mathbb{R} \to \mathbb{R}$ be a function such that

$f'(x) = (x - 2024)^3(x - 2025)(x - 2026)^2$ for all $x \in \mathbb{R}$.

Let $g: \mathbb{R} \to (0, \infty)$ be a function such that $g(x) = \sqrt{f(x)}$ for all $x \in \mathbb{R}$.

Then the number of points at which $g(x)$ has a local maximum is: