Stationary Points
Flashcard
•
Mathematics
•
10th Grade
•
Practice Problem
•
Hard
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What are stationary points in calculus?
Back
Stationary points are points on a curve where the derivative (slope) is zero, indicating a potential local maximum, minimum, or inflection point.
2.
FLASHCARD QUESTION
Front
How do you find stationary points of a function?
Back
To find stationary points, take the first derivative of the function, set it equal to zero, and solve for the variable.
3.
FLASHCARD QUESTION
Front
What is the first derivative of a function?
Back
The first derivative of a function represents the rate of change of the function with respect to its variable, indicating the slope of the tangent line at any point.
Tags
CCSS.HSF.LE.B.5
4.
FLASHCARD QUESTION
Front
What does it mean if the first derivative is positive?
Back
If the first derivative is positive, the function is increasing at that point.
5.
FLASHCARD QUESTION
Front
What does it mean if the first derivative is negative?
Back
If the first derivative is negative, the function is decreasing at that point.
Tags
CCSS.HSF.IF.B.4
6.
FLASHCARD QUESTION
Front
What is the second derivative of a function?
Back
The second derivative is the derivative of the first derivative, indicating the curvature of the function and whether it is concave up or down.
7.
FLASHCARD QUESTION
Front
How can the second derivative help identify stationary points?
Back
The second derivative test can determine the nature of stationary points: if it's positive, the point is a local minimum; if negative, a local maximum; if zero, the test is inconclusive.
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