5.1 AB MVT

Presentation

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

6.NS.B.3, 8.F.B.4, HSF-LE.A.1B

Standards-aligned

Alyson Foley

Used 41+ times

FREE Resource

10 Slides • 8 Questions

Multiple Choice

Given $x+3=x^2y$ , find $\frac{dy}{dx}$ .

$\frac{1}{x^2-2xy}$

$\frac{1}{x^2+2xy}$

$\frac{1-2xy}{x^2}$

$\frac{2xy+1}{x^2}$

Multiple Choice

Let g be a continuous function on the closed interval [-1,4], where g(-1)=-4 and g(4)=1.

Which of the following is guaranteed by the Intermediate Value Theorem (IVT)?

g(c)=-3 for at least one c between -4 and 1

g(c)=3 for at least one c between -1 and 4

g(c)=3 for at least one c between -4 and 1

g(c)=-3 for at least one c between -1 and 4

Multiple Choice

Let $f\left(x\right)=x^2-4x+5$ . Find the average rate of change of f(x) over the interval [1,5].

1/4

Multiple Choice

Let $f\left(x\right)=x^2-4x+5$ . Find the instantaneous rate of change of f(x).

$f'\left(x\right)=2x$

$f'\left(x\right)=2x-9$

$f'\left(x\right)=2x-4$

$f'\left(x\right)=2x+1$

Multiple Choice

$f\left(x\right)=x^2-4x+5$

Is there a value of x where the instantaneous rate of change of f(x) equals the average rate of change of f(x) over the interval [1,5]?

none

x=3

x = -1

x=1

Draw

For each function below, draw the segment between the indicated points on the graph. Is there a point on the graph between the indicated points where the slope of the tangent line is equal to the slope between the given points? If so, sketch the tangent line.

Draw

Match

Match the following characteristics of the IVT versus MVT.

IVT Conditions:

MVT Conditions:

Conclusion to draw in IVT problems:

Conclusion to draw in MVT problems:

Continuity

Continuity & Differentiability

Values of the function

Rate of change of the function

Vicki drove 150 miles in 3 hours. The average rate of change of her distance traveled with respect to time was 50 miles per hour.

The Mean Value Theorem tells us there must have been at least one moment in time, between noon and 3:00 pm, when she was traveling exactly 50 mph.

Determine whether you would use the IVT or MVT to answer each question.

Since v(t) is differentiable on the interval (0,9), it must be continuous. The Intermediate Value Theorem guarantees that there is a time c, for 0<c<9, such that v(c)=-1 because v(c)=-1 is between v(9)=-4 and v(0)=5.

Given $x+3=x^2y$ , find $\frac{dy}{dx}$ .

$\frac{1}{x^2-2xy}$

$\frac{1}{x^2+2xy}$

$\frac{1-2xy}{x^2}$

$\frac{2xy+1}{x^2}$

Show answer

Auto Play

Slide 1 / 18

MULTIPLE CHOICE

Similar Resources on Wayground

11 questions

Quadrilaterals

Presentation

•

9th - 12th Grade

15 questions

Finding Zeros of a Function Lesson

Presentation

•

9th - 12th Grade

11 questions

Factoring: Quadratic Trinomial when a=1

Presentation

•

9th - 12th Grade

13 questions

Solving Logarithmic Equations

Presentation

•

9th - 12th Grade

13 questions

Solving Systems w/Matrices

Presentation

•

9th - 12th Grade

13 questions

Using the Unit Circle

Presentation

•

9th - 12th Grade

13 questions

Writing Linear Functions

Presentation

•

9th - 12th Grade

12 questions

Writing Linear Equations From Two Points

Presentation

•

9th - 12th Grade

Popular Resources on Wayground

10 questions

Safety Day 2026 – Student Review

Quiz

•

9th Grade

21 questions

Continents and Oceans

Quiz

•

6th Grade

20 questions

Parts of Speech

Quiz

•

5th Grade

16 questions

Subject & Predicate

Quiz

•

5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

12 questions

Map Skills

Quiz

•

3rd Grade

22 questions

Continents and Oceans

Quiz

•

5th Grade

15 questions

Rounding Decimals

Quiz

•

5th Grade

Discover more resources for Mathematics

12 questions

Absolute Value Equations

Quiz

•

9th Grade

20 questions

Function or Not a Function

Quiz

•

8th - 9th Grade

11 questions

Slope from 2 points

Quiz

•

8th - 9th Grade

10 questions

Exploring the Basics of Exponents

Interactive video

•

6th - 10th Grade

10 questions

Solving Absolute Value Equations

Quiz

•

9th Grade

20 questions

Unit 5 Test RSC (25-26)

Quiz

•

10th Grade

18 questions

SB 12.2 Write in point slope form

Quiz

•

9th Grade

12 questions

Identify Rigid Transformations

Quiz

•

8th - 12th Grade