Concavity and Rates of Change

Flashcard
•
Mathematics
•
11th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
What is concavity in a function?
Back
Concavity refers to the direction in which a function curves. A function is concave up if its graph opens upwards (like a cup) and concave down if it opens downwards.
2.
FLASHCARD QUESTION
Front
How do you determine if a function is increasing or decreasing?
Back
A function is increasing on an interval if the derivative is positive throughout that interval. It is decreasing if the derivative is negative.
3.
FLASHCARD QUESTION
Front
What is the average rate of change of a function?
Back
The average rate of change of a function f(x) over an interval [a, b] is given by (f(b) - f(a)) / (b - a).
4.
FLASHCARD QUESTION
Front
What does it mean for a function to transition from concave down to concave up?
Back
This transition indicates a point of inflection, where the second derivative changes sign.
5.
FLASHCARD QUESTION
Front
What is the significance of the first derivative test?
Back
The first derivative test helps determine local maxima and minima of a function by analyzing the sign changes of the derivative.
6.
FLASHCARD QUESTION
Front
What is the second derivative test?
Back
The second derivative test is used to determine the concavity of a function and to identify local extrema based on the sign of the second derivative.
7.
FLASHCARD QUESTION
Front
What is an interval of increase?
Back
An interval of increase is a range of x-values where the function's output values are rising as x increases.
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