shows the concavity of the function. You can tell there is an inflection point between zero and one due to the curvature (not a quadratic curve, slows down as it comes to next critical point.

Nevertheless, the 1st derivative is zero at zero and increases and keeps on increasing till x=0.5. You can tell there is an inflection point there because the slope reverts back to zero at x=1. So, from (0,0.5), is positive, from (0.5, 1), is negative because the graph of has a negative slope at that portion. From one to two, the slope goes from zero to a large negative # with an inflection point at what looks to be two, so the second derivative is negative.

Therefore, is positive from (0, 0.5) and negative from (0.5, 2).

I hope this is right, usually I am better at this when I have a chalkboard in front of me!