I'm pretty new to derivatives and I'm not sure if I understand the concept well.
Let's say we have function $f(x) = x^2$.If we set $x=3$, our example point is set at coordinates $(3,9)$.Using formula we can find derivative of $f(x)$: $f'(x)=6$.
My question is: what does this number $6$ mean? From what I've read, it should be slope of the chosen point. Is the slope defined by one number? What is actual use of such slope?