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 $x=4$.