Mathematics

Since $f'(x) > 0$ throughout $(0,4)$, the function is strictly increasing on this interval—meaning it climbs continuously without ever leveling off or dipping. If $f(2) = 3$ and $f$ is strictly increasing, then any point to the right of $x=2$ must have a larger output value. Therefore, $f(3)$ must be strictly greater than $f(2) = 3$, so it cannot equal $3$.

Since $f'(x) > 0$ throughout $(0,4)$, the function is strictly increasing on this interval—meaning it climbs continuously without ever leveling off or dipping. If $f(2) = 3$ and $f$ is strictly increasing, then any point to the right of $x=2$ must have a larger output value. Therefore, $f(3)$ must be strictly greater than $f(2) = 3$, so it cannot equal $3$.