Any function $y=f\left(x\right)$ usually has a slope at any point of its curve that is given by the derivative $f\text{'}\left(x\right)$ of that point.
You can now also make a graph of the values of these slopes (derivatives). Here you
see the curve of a function (in red) together with the corresponding graph (in blue), the graph given by
$f\text{'}$.
The function
$f\text{'}$ is called the slope function or derivative function.
If you compare the two curves you can see that:
the values of the slope function are positive while the original function is increasing;
the values of the slope function are negative while the original function is decreasing;
at values of $x$ where the slope function has a value of $0$, the original function has a horizontal tangent; these are often extrema of the original function. .
It is therefore primarily the sign (positive, negative or $0$) of the derivative function that provides information about the curve of the original function.