Mathematics

The derivative tells you the slope of the function at each point. Since $f'(x) > 0$ everywhere on $(1,4)$, the slope is always positive—meaning as you move rightward along the interval, the function consistently climbs upward. This is the definition of a strictly increasing function, so $f$ must be increasing on $(1,4)$.

The derivative tells you the slope of the function at each point. Since $f'(x) > 0$ everywhere on $(1,4)$, the slope is always positive—meaning as you move rightward along the interval, the function consistently climbs upward. This is the definition of a strictly increasing function, so $f$ must be increasing on $(1,4)$.