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Critical Point

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AP Calculus AB/BC

Definition

A critical point is a point on a function where the derivative is either zero or undefined. It represents a potential maximum, minimum, or inflection point.

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"Critical Point" also found in:

Subjects (39)

Practice Questions (14)

What does it mean for a function to have a critical point?
If the derivative of a function is positive on the left side of a critical point and negative on its right side, what can we conclude about the critical point?
When optimizing a function, what does it mean to find a critical point?
How can you determine whether a critical point corresponds to a maximum or minimum value in an optimization problem?
What does it indicate if the derivative is negative on one side of a critical point and positive on the other side?
What does it indicate if the derivative is positive on both sides of a critical point?
What does it indicate if the derivative is negative on both sides of a critical point?
What does it mean when the y-value of a critical point is larger than the y-values of the endpoints?
What does it mean when the y-value of a critical point is smaller than the y-values of the endpoints?
If the second derivative is negative at a critical point, then the critical point corresponds to:
If the second derivative is positive at a critical point, then the critical point corresponds to:
Which of the following statements is true about a function if its second derivative is zero at a critical point?
The Second Derivative Test is used to analyze the concavity of a function and determine whether a critical point is a relative minimum, relative maximum, or neither. This test is based on the principle that:
What key feature of a function can be determined by analyzing the sign of the first derivative at a critical point?

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Critical Point

from class:

AP Calculus AB/BC

Definition

"Critical Point" also found in:

Subjects (39)

Practice Questions (14)

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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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study guides for every class

that actually explain what's on your next test

Critical Point

from class:

AP Calculus AB/BC

Definition

Related terms

"Critical Point" also found in:

Subjects (39)

Practice Questions (14)

© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.

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