Need a help on statistics pricing problem

#1
Attachement has the clear explanation

Question is

What can you conclude about the price in this problem if the probability function has (-),(+), (0) second derivatives?

Are there any other things that you could conclude about the price?

What if the quantity q was decreasing in p?
 
#2
The second derivates in this case refer to how quickly the price is changing. If the second derivative is (+), then the instantaneous price is rising. If negative, it's falling. If zero, then the revenue change is unchanging. If this seems complicated, take calculus, it's fairly intuitive.

The second question is fairly ambiguous, so I'd say it's a trick question and go with no. If the quantity is decreasing, you'd expect the price to rise. This is also basic econ.