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 f is concave up (or upwards) where the derivative f′ is increasing. This is equivalent to the derivative of f′, which is f′′, being positive. Similarly, f is concave down (or downwards) where the derivative f′ is decreasing (or equivalently, f′′ is negative).
Graphically, a graph that's concave up has a cup shape, ∪, and a graph that's concave down has a cap shape, ∩.
Want to learn more about concavity and differential calculus? Check out this video.
Practice set 1: Analyzing concavity graphically
Select all the intervals where f′(x)>0 and f′′(x)>0.