You are strongly advised to try the First derivative puzzle first.

Let be a function which is twice differentiable, with its first derivative and its second derivative function. The knowledge about gives us information about it :

(1) implies that is strictly concave upward in .
(2) implies that is strictly concave downward in .
(3) may imply that has a point of inflection at x.

Keeping these properties and that of try the examples in the puzzle. Click the button below to start the puzzle.