Critical Numbers and Extrema in Rational Functions

Critical Numbers and Extrema in Rational Functions

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Hard

Created by

Lucas Foster

FREE Resource

The video tutorial explains how to determine critical numbers for a rational function by analyzing its first derivative. It begins with defining critical numbers and their significance in finding relative extrema. The tutorial then covers determining the domain of the function, finding the derivative using the quotient rule, and analyzing where the derivative is zero or undefined. Finally, it concludes with a graph analysis to identify relative extrema, emphasizing that not all critical points are extrema.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

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

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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