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Μάθημα: AP®︎ Λογισμός BC > Ενότητα 5
Μάθημα 7: Determining concavity of intervals and finding points of inflection: algebraic- Analyzing concavity (algebraic)
- Inflection points (algebraic)
- Mistakes when finding inflection points: second derivative undefined
- Mistakes when finding inflection points: not checking candidates
- Analyzing the second derivative to find inflection points
- Analyze concavity
- Find inflection points
- Concavity review
- Inflection points review
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Inflection points review
Review your knowledge of inflection points and how we use differential calculus to find them.
What are inflection points?
Inflection points (or points of inflection) are points where the graph of a function changes concavity (from to or vice versa).
Want to learn more about inflection points and differential calculus? Check out this video.
Practice set 1: Analyzing inflection points graphically
Want to try more problems like this? Check out this exercise.
Practice set 2: Analyzing inflection points algebraically
Inflection points are found in a way similar to how we find extremum points. However, instead of looking for points where the derivative changes its sign, we are looking for points where the second derivative changes its sign.
Let's find, for example, the inflection points of .
The second derivative of is .
Let's evaluate at each interval to see if it's positive or negative on that interval.
Interval | Verdict | ||
---|---|---|---|
We can see that the graph of changes concavity at both and , so has inflection points at both of those -values.
Want to try more problems like this? Check out this exercise.
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