Open or closed intervals? Say you have a graph for v[t]
Question asks “when is speed constant”
The flat part of v[t] is from $2$ to $3$ seconds.
Is the answer $2 < t < 3$
or is it $2 \le t \le 3$ ?
$$\lim_{t\to 2} v(t)=v(2)$$ so does that mean to include or exclude 2?
I've been told to always exclude the endpoints, but you do come across some textbooks that include them.  This seems to be one of those "gray" areas ... you'll also encounter the same issue for intervals where a function is increasing, decreasing, concave upward, or concave downward ... Do I just go with the open intervals?
 A: The inclusion, or not, of the endpoints is relevant to the object of study for each situation. For example, with integration, you get the same value for $\int_{(a,b)}f$, $\int_{[a,b]}f$, or any set that differs from $[a,b]$ on finitely many* points. So for integration there's no effective difference in including the endpoints or not.
Contrarily, we could be studying global extrema of a function in an interval, and in this case it makes all the difference. We can guarantee the existence of global a maximum and minimum if we're studying the function in $[a,b]$ (Weierstrass extreme value theorem), but we cannot guarantee global extrema if the interval is open. So here we must be clear about which we are talking about.
There's many other realms where closed-ness or open-ness makes a big difference, and in much more general ways. To give a last example, take the intersection of the sets $(0,\frac1n)$ for all $n$. Clearly this is the empty set, whereas the intersection of $[0,\frac1n]$ for all $n$ is the number $0$. In fact, we can use this as a defining property of the real numbers, namely that any infinite intersection of a sequence of "nested" closed intervals contains a real number. We can not use this property if we replace closed with open.
So we must know whether the endpoints affect whatever problem we're working with. In any case, it's always more correct to write every point for which a property holds, if this is asked. So if your function is "flat" on the endpoints, I would write that.
$\small\text{*More generally, $zero$  $measure$}$
A: I think when you mean speed (or velocity) constant, the key thing is v'(t)=0. So at the endpoints in your example, the derivatives don't seem to exist (remember that right hand derivative=left hand derivative). So, yes go for the open interval
A: Since $v = dx/dt$ involves a derivative, it naturally makes sense to talk about it being constant in open intervals. 
A: To me, it seems to make sense to INCLUDE the endpoints.  v(2) = v(2.5) = v(3).  They all have the same velocity, so velocity is constant with respect to all of those times.
