First and Second Derivative Practice

First and Second Derivative Practice

Assessment

Flashcard

Mathematics

9th - 12th Grade

Practice Problem

Hard

CCSS
HSF.IF.B.4, HSF.IF.A.2

Standards-aligned

Created by

Wayground Content

FREE Resource

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the second derivative of a function used for?

Back

The second derivative is used to determine the concavity of a function and to identify points of inflection.

2.

FLASHCARD QUESTION

Front

Define concave up.

Back

A function is concave up on an interval if its second derivative is positive on that interval.

3.

FLASHCARD QUESTION

Front

Define concave down.

Back

A function is concave down on an interval if its second derivative is negative on that interval.

4.

FLASHCARD QUESTION

Front

What does a positive first derivative indicate about a function?

Back

A positive first derivative indicates that the function is increasing.

Tags

CCSS.HSF.IF.B.4

5.

FLASHCARD QUESTION

Front

What does a negative first derivative indicate about a function?

Back

A negative first derivative indicates that the function is decreasing.

6.

FLASHCARD QUESTION

Front

What is a point of inflection?

Back

A point of inflection is a point on the graph of a function where the concavity changes.

7.

FLASHCARD QUESTION

Front

How do you find the intervals of concavity for a function?

Back

To find intervals of concavity, take the second derivative of the function, set it to zero, and solve for critical points. Test intervals around these points.

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