Suppose a friend makes the following argument. A function is increasing and concave downward. Therefore, is positive and decreasing, so it eventually becomes

Suppose a friend makes the following argument. A function ƒ is increasing and concave downward. Therefore, ƒ′ is positive and decreasing, so it eventually becomes 0 and then negative, at which point ƒ decreases. Show that your friend is wrong by giving an example of a function that is always increasing and concave downward.