We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 1 : Rate of Change

Study concepts, example questions & explanations for Calculus 1

Create An Account

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : How To Find Rate Of Change

Determine the average rate of change of the function y=-cos(x) from the interval $\left[\frac{\pi}{2},\pi\right]$ .

Possible Answers:

$\frac{2}{\pi}$

$\frac{\pi}{2}$

$\pi$

Correct answer:

$\frac{2}{\pi}$

Explanation:

Write the formula to determine average rate of change.

$\frac{\Delta f}{\Delta x}= \frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$

Substitute the values and solve for the average rate of change.

$\frac{-cos(\pi)-(-cos(\frac{\pi}{2}))}{\pi-\frac{\pi}{2}} = \frac{-(-1)+0}{\frac{\pi}{2}}=\frac{1}{\frac{\pi}{2}}=\frac{2}{\pi}$

Report an Error

Example Question #2 : How To Find Rate Of Change

Find the rate of change of a function f(x)=2x-9 from $x_{1}=3$ to $x_{2}=6$ .

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

Write the formula for the average rate of change from the interval $[{x_{1},x_{2}}]$ .

$\frac{f(x_2)-f(x_{1})}{x_2-x_1}$

Solve for f(x_2) and f(x_1) .

f(x_2=6)=2(6)-9=3

f(x_1=3)=2(3)-9=-3

Substitute the known values into the formula and solve.

$\frac{f(x_2)-f(x_{1})}{x_2-x_1}=\frac{3-(-3)}{6-3}=\frac{6}{3}=2$

Report an Error

Example Question #3 : Rate Of Change

Suppose the rate of a square is increasing at a constant rate of meters per second. Find the area's rate of change in terms of the square's perimeter.

Possible Answers:

$2\sqrt2P$

$\frac{1}{4}P$

$\frac{1}{2}P$

Correct answer:

Explanation:

Since the question is asking for the rate of change in terms of the perimeter, write the formula for the perimeter of the square and differentiate it with the respect to time.

P=4s

$\frac{dP}{dt}= 4\frac{ds}{dt}$

The question asks in terms of the perimeter. Isolate the term by dividing four on both sides.

$s=\frac{P}{4}$

Write the given rate in mathematical terms and substitute this value into $\frac{dP}{dt}$ .

$\frac{ds}{dt}=2$

$\frac{dP}{dt}= 4\frac{ds}{dt}=4(2)=8$

Write the area of the square and substitute the side.

$A=s^2=\left(\frac{P}{4}\right)^2=\frac{P^2}{16}$

Since the area is changing with time, take the derivative of the area with respect to time.

$\frac{dA}{dt}=\frac{P}{8} \cdot \frac{dP}{dT}$

Substitute the value of $\frac{dP}{dt}$ .

$\frac{dA}{dt}=\frac{P}{8} \cdot 8=P$

Report an Error

Example Question #4 : Rate Of Change

Determine the point on the function that is not changing: y=x^2-36x+6

Possible Answers:

(6,36)

(0,6)

(36.6)

(18,-318)

(18,6)

Correct answer:

(18,-318)

Explanation:

In order to determine where the function is not changing, it is necessary to take the derivative and set the slope equal to zero. This will provide information on where the curve is not changing. Once we find the x value that gives the derivative a slope of zero, we can substitute the x-value back into the original function to obtain the point.

y=x^2-36x+6

y'=2x-36

0=2x-36

36=2x

x=18

Substitute this value back to the original equation to solve for .

y=18^2-36(18)+6 = 324-648+6 = -318

The point where the function is not changing is (18,-318) .

Report an Error

Example Question #1 : How To Find Rate Of Change

For the function y=10 , what is the average rate of change from x=1 to x=3 ?

Possible Answers:

Correct answer:

Explanation:

Write the formula for average rate of change.

$\frac{f(x_f)-f(x_i)}{x_f-x_i}$

Determine the values of x_f and x_i .

f(x_f)=f(x_i)=10

x_i=1

x_f=3

Substitute the known values.

$\frac{f(x_f)-f(x_i)}{x_f-x_i}=\frac{10-10}{3-1}=0$

Report an Error

Example Question #2 : How To Find Rate Of Change

Find the rate of change of a function f(x)=5x+9 from x_1=4 to x_2=6 .

Possible Answers:

Correct answer:

Explanation:

We can solve by utilizing the formula for the average rate of change: $\frac{f(x_2)-f(x_1)}{x_2-x_1}.$ Solving for f(x) at our given points:

f(x_1)=f(4)=5(4)+9=20+9=29

f(x_2)=f(6)=5(6)+9=30+9=39

Plugging our values into the average rate of change formula, we get:

$\frac{(39-29)}{(6-4)}=\frac{10}{2}=5$

Report an Error

Example Question #5 : Rate Of Change

Find the rate of change of a function f(x)=9x+7 from x_1=7 to x_2=8

Possible Answers:

Correct answer:

Explanation:

We can solve by utilizing the formula for the average rate of change: $\frac{f(x_2)-f(x_1)}{x_2-x_1}}$ . Solving for f(x) at our given points:

f(x_1)=f(7)=9(7)+7=63+7=70

f(x_2)=f(8)=9(8)+7=72+7=79

Plugging our values into the average rate of change formula, we get:

$\frac{(79-70)}{(8-7)}=\frac{9}{1}=9$

Report an Error

Example Question #6 : Rate Of Change

Find the rate of change of a function f(x)=3x+7 from x_1=2 to x_2=3 .

Possible Answers:

Correct answer:

Explanation:

We can solve by utilizing the formula for the average rate of change: $\frac{f(x_2)-f(x_1) }{x_2-x_1}$ . Solving for f(x) at our given points:

f(x_1)=f(2)=3(2)+7=6+7=13

f(x_2)=f(3)=3(3)+7=9+7=16

Plugging our values into the average rate of change formula, we get:

$\frac{(16-13)}{(3-2)}=\frac{3}{1}=3$

Report an Error

Example Question #3 : How To Find Rate Of Change

Find the rate of change of a function f(x)=4x+9 from x_1=1 to x_2=2 .

Possible Answers:

Correct answer:

Explanation:

We can solve by utilizing the formula for the average rate of change:

$\frac{ f(x_2)-f(x_1)}{x_2-x_1}$ .

Solving for f(x) at our given points:

f(x_1)=f(1)=4(1)+9=4+9=13

f(x_2)=f(2)=4(2)+9=8+9=17

Plugging our values into the average rate of change formula, we get:

$\frac{17-13}{2-1}=\frac{4}{1}=4$

Report an Error

Example Question #4 : How To Find Rate Of Change

Find the rate of change of a function f(x)=6x-7 from x_1=5 to x_2=6 .

Possible Answers:

Correct answer:

Explanation:

We can solve by utilizing the formula for the average rate of change:

$\frac{ f(x_2)-f(x_1)}{x_2-x_1}$ .

Solving for f(x) at our given points:

f(x_1)=f(5)=6(5)-7=30-7=23

f(x_2)=f(6)=6(6)-7=36-7=29

Plugging our values into the average rate of change formula, we get:

$\frac{29-23}{6-5}=\frac{6}{1}=6$

Report an Error

View Calculus Tutors

James
Certified Tutor

Kennesaw State University, Master of Science, Statistics.

View Calculus Tutors

Benjamin
Certified Tutor

Portland State University, Bachelor of Science, Computer Science.

View Calculus Tutors

Naman Sanjaykumar
Certified Tutor

LDRP Institute of Technology and Research, Bachelor, Mechanical Engineering. University of Windsor, Master's/Graduate, Mechan...

All Calculus 1 Resources

10 Diagnostic Tests 438 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Physics Tutors in Los Angeles, French Tutors in Phoenix, SSAT Tutors in Los Angeles, French Tutors in San Diego, Computer Science Tutors in Philadelphia, Algebra Tutors in Miami, Algebra Tutors in Seattle, English Tutors in Chicago, Physics Tutors in San Francisco-Bay Area, Physics Tutors in New York City

Popular Courses & Classes

ISEE Courses & Classes in Phoenix, ISEE Courses & Classes in New York City, ISEE Courses & Classes in Denver, LSAT Courses & Classes in Miami, GRE Courses & Classes in Atlanta, LSAT Courses & Classes in Washington DC, ACT Courses & Classes in Dallas Fort Worth, GRE Courses & Classes in Boston, LSAT Courses & Classes in Dallas Fort Worth, MCAT Courses & Classes in Washington DC

Popular Test Prep

GRE Test Prep in Atlanta, LSAT Test Prep in Los Angeles, MCAT Test Prep in Los Angeles, MCAT Test Prep in Phoenix, GRE Test Prep in Boston, SAT Test Prep in Chicago, ISEE Test Prep in Denver, SAT Test Prep in Boston, SSAT Test Prep in Boston, ACT Test Prep in Los Angeles

DMCA Complaint

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.

Send your complaint to our designated agent at:

Charles Cohn Varsity Tutors LLC
101 S. Hanley Rd, Suite 300
St. Louis, MO 63105

Or fill out the form below:

Do not fill in this field

Contact Information

* Full legal name

Company name

* Phone number

* Email address

Address

* Address1

Address2

* City

* State

* Zipcode

* Country

Complaint Details

* URL of copyrighted work (where your original material is located)

* Please describe the copyrighted work so that it may be easily identified

I am the owner, or an agent authorized to act on behalf of the owner of an exclusive right that is allegedly infringed.

I have a good faith belief that the use of the material in the manner complained of is not authorized by the copyright owner, its agent, or the law.

This notification is accurate.

I acknowledge that there may be adverse legal consequences for making false or bad faith allegations of copyright infringement by using this process.

* Signature (your digital signature is legally binding)

HIGH SCHOOL

GRADUATE SCHOOL

K-8

Search 50+ Tests

math tutoring

science tutoring

foreign languages

elementary tutoring

other

Search 350+ Subjects

Calculus 1 : Rate of Change

Study concepts, example questions & explanations for Calculus 1

All Calculus 1 Resources

Example Questions

Example Question #1 : How To Find Rate Of Change

Example Question #2 : How To Find Rate Of Change

Example Question #3 : Rate Of Change

Example Question #4 : Rate Of Change

Example Question #1 : How To Find Rate Of Change

Example Question #2 : How To Find Rate Of Change

Example Question #5 : Rate Of Change

Example Question #6 : Rate Of Change

Example Question #3 : How To Find Rate Of Change

Example Question #4 : How To Find Rate Of Change

All Calculus 1 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: