

Analyzing Derivatives and Extrema
Interactive Video
•
Mathematics
•
9th - 10th Grade
•
Practice Problem
•
Hard
Thomas White
FREE Resource
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15 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the main objective of the problem discussed in the video?
To solve the equation for x
To calculate the area under the curve
To determine the relative extremes and points of inflection
To find the maximum value of the curve
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first derivative of the given curve?
x^3 - 3x^2
2x^2 + 3x
12x^2 - 12x
4x^3 - 6x^2
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
At which x-values are the possible extreme points identified?
x = 0 and x = 3/2
x = 2 and x = 3
x = 1 and x = 2
x = -1 and x = 1
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the second derivative of the curve?
12x^2 - 12x
4x^3 - 6x^2
x^3 - 3x^2
2x^2 + 3x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What condition is used to identify a point of inflection?
The second derivative is zero
The first derivative is zero
The function value is zero
The third derivative is zero
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the change in concavity around x = 0 determined?
By calculating the first derivative
By checking the sign change in the second derivative
By evaluating the third derivative
By plotting the graph
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is concluded about x = 0 in terms of inflection?
It is not an inflection point
It is an inflection point
It is a local minimum
It is a local maximum
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