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, $\cup$, and a graph that's concave down has a cap shape, $\cap$.