Using theorem or FunctionChart.

Jarekkk — Fri, 10 Feb 2012 03:00:55 Z

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)...

MaplePrimes - answers and comments on Question, concavity of a function

Using theorem or FunctionChart.