
AP Calc BC Unit I
Flashcard
•
Mathematics
•
11th - 12th Grade
•
Practice Problem
•
Hard
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1.
FLASHCARD QUESTION
Front
What does it mean for a function's derivative to be always negative?
Back
If a function's derivative is always negative, it means that the function is decreasing for all values in its domain.
2.
FLASHCARD QUESTION
Front
What is the relationship between a function and its derivative?
Back
The derivative of a function represents the rate of change of the function. If the derivative is positive, the function is increasing; if negative, the function is decreasing.
3.
FLASHCARD QUESTION
Front
Define critical points of a function.
Back
Critical points are values in the domain of a function where the derivative is either zero or undefined. They are potential locations for local maxima and minima.
4.
FLASHCARD QUESTION
Front
What is the Mean Value Theorem?
Back
The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).
5.
FLASHCARD QUESTION
Front
Explain the concept of concavity.
Back
Concavity refers to the direction in which a curve bends. A function is concave up if its second derivative is positive, and concave down if its second derivative is negative.
6.
FLASHCARD QUESTION
Front
What is the significance of inflection points?
Back
Inflection points are points on the graph of a function where the concavity changes. They occur where the second derivative is zero or undefined.
7.
FLASHCARD QUESTION
Front
How do you determine if a function is increasing or decreasing?
Back
A function is increasing on an interval if its derivative is positive throughout that interval, and decreasing if its derivative is negative.
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