Concavity and Rates of Change

Concavity and Rates of Change

Assessment

Flashcard

Mathematics

11th Grade

Hard

Created by

Wayground Content

FREE Resource

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15 questions

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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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