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Do you count undefined points in the concavity?

Question:

Do you count undefined points in the concavity?

Functions:


For a function {eq}y=f(x) {/eq} defined in the Cartesian plane, the first derivative test tells us about the increasing/decreasing nature of the function whereas the second derivative test for a function tells us about the concavity, as well as the inflection points of a function, i.e. the points at which the second derivative is zero or undefined.

Answer and Explanation:


As we know that the concavity is calculated by the second derivative test. For a function, whose second derivative at a point is positive, we can say the concavity of that function to be upward at that point, whereas for a function whose second derivative is negative at a point, we can say the concavity to be downward at that point.

Now, the inflection point is a point at which the second derivative is undefined or zero.

Hence, concavity does not counts the undefined points, rather it counts the curvature of the function.


Learn more about this topic:

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Concavity and Inflection Points on Graphs

from Math 104: Calculus

Chapter 9 / Lesson 5
7.5K

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