Review your knowledge of concavity of functions and how we use differential calculus to analyze it.

What is concavity?

Concavity relates to the rate of change of a function's derivative. A function ff is concave up (or upwards) where the derivative ff' is increasing. This is equivalent to the derivative of ff', which is ff'', being positive. Similarly, ff is concave down (or downwards) where the derivative ff' is decreasing (or equivalently, ff'' is negative).
Graphically, a graph that's concave up has a cup shape, \cup, and a graph that's concave down has a cap shape, \cap.
Want to learn more about concavity and differential calculus? Check out this video.

Practice set 1: Analyzing concavity graphically

Want to try more problems like this? Check out this exercise.

Practice set 2: Analyzing concavity algebraically

Want to try more problems like this? Check out this exercise.
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