What is the first step in determining relative extrema using the second derivative test?

Understanding Relative Extrema and the Second Derivative Test

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard

Ethan Morris
FREE Resource
Read more
10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Graph the function to find extrema.
Evaluate the function at various points.
Determine the critical numbers where the first derivative is zero or undefined.
Find the second derivative of the function.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you find the critical numbers of a function?
By setting the second derivative equal to zero.
By finding where the first derivative is zero or undefined.
By evaluating the function at x = 0.
By graphing the function.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does a positive second derivative at a critical number indicate?
The function has a point of inflection.
The function is concave up, indicating a relative minimum.
The function is concave down, indicating a relative maximum.
The function is undefined at that point.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the second derivative of the function given in the example?
12x^2 - 8x
4x^3 - 4x^2
8x^2 - 12x
4x^2 - 8x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of evaluating the second derivative at x = 1?
The second derivative is undefined.
The second derivative is positive.
The second derivative is negative.
The second derivative is zero.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the relative minimum value of the function at x = 1?
-1/3
1
0
1/3
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the graph of the function indicate about the point at x = 0?
There is a relative maximum.
The function is undefined.
There is a relative minimum.
There is no relative extrema.
Create a free account and access millions of resources
Similar Resources on Wayground
11 questions
Critical Numbers in Rational Functions

Interactive video
•
10th - 12th Grade
11 questions
Understanding Relative Extrema in Functions

Interactive video
•
9th - 12th Grade
11 questions
Understanding the Second Derivative Test

Interactive video
•
10th - 12th Grade
7 questions
Graphing Functions with Calculators

Interactive video
•
9th - 12th Grade
11 questions
Understanding Relative Extrema Using the First Derivative Test

Interactive video
•
10th - 12th Grade
11 questions
Understanding Derivatives and Critical Points

Interactive video
•
10th - 12th Grade
11 questions
Understanding Absolute Extrema

Interactive video
•
10th - 12th Grade
11 questions
Critical Numbers and Extrema in Rational Functions

Interactive video
•
10th - 12th Grade
Popular Resources on Wayground
25 questions
Equations of Circles

Quiz
•
10th - 11th Grade
30 questions
Week 5 Memory Builder 1 (Multiplication and Division Facts)

Quiz
•
9th Grade
33 questions
Unit 3 Summative - Summer School: Immune System

Quiz
•
10th Grade
10 questions
Writing and Identifying Ratios Practice

Quiz
•
5th - 6th Grade
36 questions
Prime and Composite Numbers

Quiz
•
5th Grade
14 questions
Exterior and Interior angles of Polygons

Quiz
•
8th Grade
37 questions
Camp Re-cap Week 1 (no regression)

Quiz
•
9th - 12th Grade
46 questions
Biology Semester 1 Review

Quiz
•
10th Grade