## Calculus: Early Transcendentals (2nd Edition)

Because the function that is positive at some $x$ can be both decreasing and increasing.
The sign of $f'(x)$ shows if the function is increasing or decreasing at that $x$. if $f'(x)>0$ then the function is increasing and $f'(x)<0$ then the function is decreasing. It doesn't matter if the function is positive at some $x$ it can be both decreasing and increasing so $f'(x)$ can be both positive and negative.