What is a critical number in the context of a rational function?

Critical Numbers and Extrema in Rational Functions

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

Lucas Foster
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A point where the first derivative is zero or undefined
A point where the function has a maximum value
A point where the function is not defined
A point where the second derivative is zero
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is it important to determine the domain of a rational function?
To determine where the function is not defined
To identify where the function is continuous
To calculate the function's maximum value
To find the range of the function
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in finding the derivative of a rational function using the quotient rule?
Square the denominator of the original function
Multiply the numerator by the derivative of the denominator
Add the numerator and denominator
Subtract the derivative of the numerator from the denominator
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When is a derivative considered undefined?
When both numerator and denominator are zero
When the denominator is zero
When the function is continuous
When the numerator is zero
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the critical number of the function discussed in the video?
x = 0
x = 1
x = -5
x = -1
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why can't x = -1 be a critical number for the function?
Because it makes the numerator zero
Because it is a maximum point
Because it is a point of discontinuity
Because it is not in the domain of the function
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the presence of a critical number indicate about a function?
The function has a relative minimum
The function has a relative maximum
The function is undefined at that point
The function may have a relative extrema
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