I know about two possible ways.
1) Applying the theorem that the function is concave if its second derivative is negative (or non-positive).
2) You can also use the command ?Student[Calculus1][FunctionChart] with which you plot the function with ilustrated properties.
For your function, the 2) would look like this:
In school we learnt that the function is convex if its second derivative is positive (or non-negative) and concave if its second derivative is negative (non-positive). When I looked at the help (and the internet) I realised that convex function is also called concave up ...
According to this Maple command I also have a question. Why am I getting this graph for f(t)=1/t?
This function is concave (or concave down) on (-infinity,0)...