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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)

AP Chemistry
Advanced Chemical Engineering Science
Algebraic Topology
Analytic Combinatorics
Analytic Geometry and Calculus
Atomic Physics
Biophysical Chemistry
Calculus IV
Cohomology Theory
College Physics: Thermodynamics, Electricity, and Magnetism
Computational Geometry
Control Theory
Differential Calculus
Dynamical Systems
Elementary Differential Topology
Geometric Measure Theory
Geothermal Systems Engineering
Heat and Mass Transfer
High Energy Density Physics
Honors Physics
Honors Pre-Calculus
Intro to Chemistry
Intro to College Physics
Introduction to Mathematical Analysis
Introduction to Mathematical Economics
Metric Differential Geometry
Molecular Physics
Morse Theory
Nonlinear Control Systems
Nonlinear Optimization
Physical Chemistry I
Physical Chemistry II
Power System Stability and Control
Separation Processes
Statistical Mechanics
Thermodynamics
Thermodynamics I
Thermodynamics II
Thermodynamics of Fluids

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

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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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