Learn how to use the second derivative test to determine relative extrema

The video tutorial explains how to use the second derivative test to determine the concavity of a function and identify relative minima. It begins with taking the first derivative and finding critical values, then discusses the first derivative test. The focus shifts to the second derivative test, explaining how to find and evaluate the second derivative. The tutorial concludes with a justification of the test's results, emphasizing the importance of understanding the test's application and implications.

What is the first step in using the second derivative test?

• Find the second derivative

• Evaluate the function at a point

• Take the first derivative

• Determine the concavity

What is the critical value found in the first section?

• X = 1/2

• X = -3/2

• X = 3

• X = 2

What is the value of the second derivative in this example?

• 0

• 1

• 2

• 3

What does a positive second derivative indicate about the graph?

• The graph is concave up

• The graph is concave down

• The graph has a relative maximum

• The graph is linear

According to the second derivative test, what does F(x) have at X = -3/2?

• A relative maximum

• A relative minimum

• An inflection point

• No critical point