Second derivative test  Using derivatives to analyze functions  AP Calculus AB  Khan Academy  Summary and Q&A
TL;DR
The second derivative test helps determine if a function has a maximum or minimum value at a given point based on the concavity of the function.
Questions & Answers
Q: What does the second derivative test help determine?
The second derivative test helps determine if a function has a maximum or minimum value at a given point based on the concavity of the function.
Q: How can you identify a relative maximum point using the second derivative test?
To identify a relative maximum point, check if the slope of the tangent line is zero and if the concavity is decreasing towards the point.
Q: What does a relative minimum point look like according to the second derivative test?
A relative minimum point has a slope of zero and concavity increasing towards the point.
Q: What does a second derivative less than zero indicate?
If the second derivative is less than zero, it indicates a relative maximum point.
Summary & Key Takeaways

The second derivative test analyzes the concavity and slope of a function to determine if a point is a relative maximum or minimum.

A relative maximum point is characterized by a slope of zero and concavity decreasing towards the point, while a relative minimum point has a slope of zero and concavity increasing towards the point.

If the second derivative is less than zero, it indicates a relative maximum point, and if it is greater than zero, it indicates a relative minimum point.