We are open Saturday and Sunday!

Call Now to Set Up Tutoring:

(888) 888-0446

AP Calculus AB : Corresponding characteristics of graphs of ƒ and ƒ'

Study concepts, example questions & explanations for AP Calculus AB

Create An Account

All AP Calculus AB Resources

3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Calculus I — Derivatives

The speed of a car traveling on the highway is given by the following function of time:

f(t) = 5t^2+2t

Consider a second function:

g(t) = 10t+2

What can we conclude about this second function?

Possible Answers:

It represents the rate at which the speed of the car is changing.

It represents the change in distance over a given time .

It has no relation to the previous function.

It represents the total distance the car has traveled at time .

It represents another way to write the car's speed.

Correct answer:

It represents the rate at which the speed of the car is changing.

Explanation:

Notice that the function g(t) is simply the derivative of f(t) with respect to time. To see this, simply use the power rule on each of the two terms.

f'(t) = (2)(5)t + 2 = g(t)

Therefore, g(t) is the rate at which the car's speed changes, a quantity called acceleration.

Report an Error

Example Question #1 : Corresponding Characteristics Of Graphs Of ƒ And ƒ'

Find the critical numbers of the function,

$f(x)=\frac{1+x^2}{x}$

Possible Answers:

$x =\left \{ -1,0,1\right \}$

$x =\left \{ -1\right \}$

$x =\left \{ 1\right \}$

$x =\left \{ -1,1\right \}$

Correct answer:

$x =\left \{ -1,1\right \}$

Explanation:

$f(x)=\frac{1+x^2}{x}$

1) Recall the definition of a critical point:

The critical points of a function f(x) are defined as points (a,f(a)) , such that x=a is in the domain of f(x) , and at which the derivative f'(a) is either zero or does not exist. The number x=a is called a critical number of f(x) .

2) Differentiate ,

$f'(x)=\frac{d}{dx}\left(\frac{1+x^2}{x} \right )=\frac{d}{dx}\left(\frac{1}{x}+x \right )=-\frac{1}{x^2}+1$

3) Set to zero and solve for ,

$f'(x)=-\frac{1}{x^2}+1= 0$

$\frac{1}{x^2}=1$

The critical numbers are,

$x =\left \{ -1,1\right \}$

We can also observe that the derivative does not exist at x = 0 , since the $-\frac{1}{x^2}$ term would be come infinite. However, is not a critical number because the original function f(x) is not defined at x=0 . The original function is infinite at x=0 , and therefore x = 0 is a vertical asymptote of f(x) as can be seen in its' graph,

Problem 7 plot

Further Discussion

In this problem we were asked to obtain the critical numbers. If were were asked to find the critical points, we would simply evaluate the function f(x) at the critical numbers to find the corresponding function values and then write them as a set of ordered pairs,

$\left \{(-1,-2), (1,2) \right \}$

Report an Error

Example Question #2 : Corresponding Characteristics Of Graphs Of ƒ And ƒ'

The function f(x) is a continuous, twice-differentiable functuon defined for all real numbers.

If the following are true:

Which function could be f(x) ?

Possible Answers:

sin(x)

e^x

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

ln(x)

Correct answer:

ln(x)

Explanation:

To answer this problem we must first interpret our given conditions:

Implies the function is strictly increasing.
Implies the function is strictly concave down.

We note the only function given which fufills both of these conditions is lnx .

Report an Error

Example Question #3 : Corresponding Characteristics Of Graphs Of ƒ And ƒ'

A jogger leaves City at t=0 . His subsequent position, in feet, is given by the function:

$x(t) = 5t^{2} - 3t + 2$ ,

where is the time in minutes.

Find the acceleration of the jogger at t=15 minutes.

Possible Answers:

$10\ ft/min$

$10\ ft/min^{2}$

$10\ ft$

$147\ ft/min^{2}$

$147\ ft/min$

Correct answer:

$10\ ft/min^{2}$

Explanation:

The accelaration is given by the second derivative of the position function:
a(t) = f''(t)

For the given position function:

$f(t) = 5t^{2} - 3t + 2$ ,

f'(t) = 10t - 3 ,

f''(t) = 10 .

Therefore, the acceleration at t=15 minutes is $10\ ft/min^{2}$ . Again, note the units must be in $ft/min^{2}$ .

Report an Error

View AP Calculus AB Tutors

Muhammad
Certified Tutor

The University of Texas at Dallas, Bachelor of Science, Mechanical Engineering.

View AP Calculus AB Tutors

Pavan
Certified Tutor

University of Tennessee, Knoxville, Master's/Graduate, Mechanical Engineering. Pennsylvania State University, Master's/Gradua...

View AP Calculus AB Tutors

Omar
Certified Tutor

Arizona State University, Bachelors, Civil Engineering.

All AP Calculus AB Resources

3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Math Tutors in Atlanta, Reading Tutors in Dallas Fort Worth, LSAT Tutors in Miami, SAT Tutors in Atlanta, Spanish Tutors in Miami, English Tutors in Seattle, SAT Tutors in Philadelphia, Math Tutors in Chicago, French Tutors in Miami, SSAT Tutors in Dallas Fort Worth

Popular Courses & Classes

ISEE Courses & Classes in Chicago, GRE Courses & Classes in Houston, SSAT Courses & Classes in Seattle, MCAT Courses & Classes in Seattle, LSAT Courses & Classes in Miami, GRE Courses & Classes in San Diego, GRE Courses & Classes in Miami, SAT Courses & Classes in New York City, LSAT Courses & Classes in New York City, MCAT Courses & Classes in San Diego

Popular Test Prep

SSAT Test Prep in Miami, SAT Test Prep in Philadelphia, GRE Test Prep in Miami, SSAT Test Prep in Atlanta, MCAT Test Prep in Washington DC, MCAT Test Prep in San Diego, ISEE Test Prep in Philadelphia, MCAT Test Prep in Boston, LSAT Test Prep in Miami, ACT Test Prep in Seattle

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

AP Calculus AB : Corresponding characteristics of graphs of ƒ and ƒ'

Study concepts, example questions & explanations for AP Calculus AB

All AP Calculus AB Resources

Example Questions

Example Question #11 : Calculus I — Derivatives

Example Question #1 : Corresponding Characteristics Of Graphs Of ƒ And ƒ'

Example Question #2 : Corresponding Characteristics Of Graphs Of ƒ And ƒ'

Example Question #3 : Corresponding Characteristics Of Graphs Of ƒ And ƒ'

All AP Calculus AB Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: