What is concavity of a graph

The video tutorial explains the concept of concavity in mathematics, focusing on concave up and concave down. It uses visual analogies like cups and water to help understand the concept. The tutorial also provides a formal mathematical definition, explaining how the slope of a function's derivative indicates concavity. The video concludes with an analysis of slopes to determine whether a function is concave up or down.

What does it mean for a graph to be concave up?

How can you visually remember the difference between concave up and concave down?

What is the mathematical definition of a function being concave up?

Explain how the slopes of a function indicate whether it is concave up or concave down.

What happens to the slope of a function when it is concave down?