Are Corners Inflection Points on a Graph?

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The answer is no, they are not critical points, but I'm not sure the reasoning carries over to corners.In summary, the conversation discusses the relationship between corners and inflection points on a graph and whether corners can also be considered inflection points. The conclusion is that corners cannot be considered inflection points due to the fact that they do not have a defined second derivative.
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karush
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MHB
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in that at corners are not differentiable, does this mean that they also are not inflection points but at the same time a change in the rate.

https://www.physicsforums.com/attachments/517
on the graph above f(x) for [0,7] at x=4 and x=5 what is f' and f'' or does it not exist

thanks ahead(Dull)
 
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From what I have read, an inflection point is a point at which the curvature or concavity changes sign. Since curvature is only defined where the second derivative exists, I think you can rule out corners from being inflection points.

Great question, by the way! It reminds me of the question of whether, given a function defined on a closed interval, whether the endpoints are critical points (since the two-sided derivative does not exist there).
 

FAQ: Are Corners Inflection Points on a Graph?

What are inflection points?

Inflection points are points on a curve where the curvature changes sign, meaning the curve changes from concave to convex or vice versa. In other words, the slope of the curve changes direction at an inflection point.

Are all corners inflection points?

No, not all corners are inflection points. Inflection points occur when the slope of the curve changes, while corners are sharp points where the curve changes direction abruptly without a change in slope. Some corners may also be inflection points, but not all.

Can corners be inflection points?

Yes, some corners can also be inflection points. This occurs when the corner is sharp enough to cause a change in slope, resulting in a change in curvature. However, not all corners are inflection points.

How can you determine if a corner is an inflection point?

To determine if a corner is an inflection point, you can look at the curvature of the curve at that point. If the curvature changes sign at the corner, then it can be considered an inflection point. Additionally, you can also look at the slope of the curve to see if it changes direction at the corner.

Are inflection points important in scientific research?

Yes, inflection points are important in scientific research because they can provide valuable information about the behavior of a curve or function. They can also help identify critical points, such as maximum or minimum points, and aid in understanding the overall shape and behavior of a curve.

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