Concavity and Inflection Points (8.3.1)

Question 1

• The concavity of a graph can be determined by using the second derivative.

Answer 1

• The concavity of a graph can be determined by using the second derivative.

Question 2

• If the second derivative of a function is positive on a given interval, then the graph of the function is concave up on that interval. If the second derivative of a function is negative on a given interval, then the graph of the function is concave down on that interval.

Answer 2

• If the second derivative of a function is positive on a given interval, then the graph of the function is concave up on that interval. If the second derivative of a function is negative on a given interval, then the graph of the function is concave down on that interval.

Question 3

• Points where the graph changes concavity are called inflection points.

Answer 3

• Points where the graph changes concavity are called inflection points.