Notice that the clues describe $f^\prime(x)$, yet you are asked to sketch $f(x)$.

$f^\prime(x) > 0$ on $1 < x < 4$
Translate: $f(x)$ is increasing between $x = 1$ and $x = 4$.

$f^\prime(x) < 0$ on $x < 1$ and $x > 4$
Translate: $f(x)$ is decreasing before $x = 1$ and after $x = 4$.

$f^\prime(x) = 0$ for $x = 1$, $x = 4$
Translate: $x$ has reached a local maximum or local minimum at $x = 1$ and $x = 4$.