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 visual analogy is used to describe a concave up function?

• A frown

• A cup

• A valley

• A mountain

Which of the following indicates that a function is concave up?

• The function's derivative is zero

• The function's derivative is decreasing

• The function's derivative is constant

• The function's derivative is increasing

If the slope of a function's derivative is becoming less negative, what can be inferred about the function?

• The function is linear

• The function is concave up

• The function is concave down

• The function is constant

What happens to the slope of a function's derivative when the function is concave down?

• The slope becomes more positive

• The slope becomes less positive

• The slope becomes zero

• The slope remains constant

Which of the following is true for a function that is concave down?

• The derivative is increasing

• The derivative is decreasing

• The derivative is zero

• The derivative is constant