For which point of inflection does the first derivative exist?

Question:

For which point of inflection does the first derivative exist?

Point of inflection

The point of inflection is the point where the concavity changes i.e when the double derivative is 0 or the curvature changes its sign from positive to negative or vice versa.

Answer and Explanation:

The point of inflection does exist for every function which is continuous at every point and the slope for some delta value both in the positive and negative direction of x is the same at that x.


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Concavity and Inflection Points on Graphs

from Math 104: Calculus

Chapter 9 / Lesson 5
7.5K

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