Understanding Rolle's Theorem

Understanding Rolle's Theorem

Assessment

Interactive Video

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
HSF.IF.A.2

Standards-aligned

Created by

Lucas Foster

FREE Resource

Standards-aligned

CCSS.HSF.IF.A.2
The video tutorial explains how to apply Rolle's Theorem to a given function on a closed interval. It begins by introducing the function and the theorem, then provides a detailed explanation of the theorem's conditions. The tutorial proceeds to apply the theorem to the function, verifying the necessary conditions and calculating the derivative. Finally, it solves for the value of C where the derivative equals zero, confirming the solution graphically.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the function given in the problem?

f(x) = x^(1/2) - x

f(x) = x + x^(1/2)

f(x) = x - x^(1/2)

f(x) = x^2 - x

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Which of the following is NOT a condition for Rolle's Theorem?

The function values at the endpoints must be equal.

The function must be differentiable on an open interval.

The function values at the endpoints must be different.

The function must be continuous on a closed interval.

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does Rolle's Theorem guarantee if its conditions are met?

The function has a maximum at the midpoint.

The function is increasing throughout the interval.

There is at least one point where the derivative is zero.

The function is decreasing throughout the interval.

Tags

CCSS.HSF.IF.A.2

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What are the values of f(0) and f(1) for the given function?

f(0) = 0, f(1) = 1

f(0) = 1, f(1) = 0

f(0) = 1, f(1) = 1

f(0) = 0, f(1) = 0

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the graphical significance of the point where the derivative is zero?

The function has a vertical tangent line.

The function has a horizontal tangent line.

The function has a discontinuity.

The function has a point of inflection.

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the derivative of the function expressed?

f'(x) = 1 + 1/2x^(1/2)

f'(x) = 1 - 1/2x^(1/2)

f'(x) = 1 - 1/2x^(-1/2)

f'(x) = 1 + 1/2x^(-1/2)

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the value of c where the derivative is zero?

c = 1/2

c = 1/3

c = 1/5

c = 1/4

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