Second derivative test | Using derivatives to analyze functions | AP Calculus AB | Khan Academy | Summary and Q&A

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July 27, 2016
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Second derivative test | Using derivatives to analyze functions | AP Calculus AB | Khan Academy

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.

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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.