Call Now to Set Up Tutoring:

(888) 888-0446

Calculus 2 : Derivative at a Point

Study concepts, example questions & explanations for Calculus 2

Create An Account

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 Next →

Example Question #103 : Derivatives

Find the derivative of the following function at x=2 :

$h(x)=2x\sin(x)$

Possible Answers:

$2\sin(2)+4\cos(2)$

$2\sin(2)-4\cos(2)$

$2\cos(2)$

$2\sin(2)$

Correct answer:

$2\sin(2)+4\cos(2)$

Explanation:

The derivative of the function is given by the product rule:

h(x)=f(x)g(x) , h'(x)=f'(x)g(x)+f(x)g'(x)

Simply find the derivative of each function:

$\frac{d}{dx}(2x)=2$

$\frac{d}{dx}\sin(x)=\cos(x)$

The derivatives were found using the following rules:

$\frac{d}{dx}\sin(x)=\cos(x)$ , $\frac{d}{dx}(x^n)=nx^{n-1}$

Simply evaluate each derivative and the original functions at the point given, using the above product rule.

Report an Error

Example Question #104 : Derivatives

Find the derivative of the following function about the point (0, 1) :

$f(x)=3x^2+\cos(x)$

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is

$f'(x)=6x-\sin(x)$

and was found using the following rules:

$\frac{d}{dx}(x^n)=nx^{n-1}$ , $\frac{d}{dx}\cos(x)= -\sin(x)$

Next, plug in the point we were asked to find the derivative at to finish the problem:

$6(0)-\sin(0)=0$

Report an Error

Example Question #105 : Derivatives

What is the slope of a function $f(x)=2x^{2}-5x+18$ at the point (3,4) ?

Possible Answers:

Correct answer:

Explanation:

By definition, slope is the first derivative of a given function f(x) .

Since $f(x)=2x^{2}-5x+18$ here, we can use the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ to derive

$f'(x)=(2)2x^{2-1}-(1)5x^{1-1}+(0)18=4x-5$ .

At (3,4) , x=3 and therefore the slope

f'(3)=4(3)-5=12-5=7 .

Report an Error

Example Question #106 : Derivatives

What is the slope of a function $f(x)=4x^{2}+x-11$ at the point (-2,5) ?

Possible Answers:

Correct answer:

Explanation:

By definition, slope is the first derivative of a given function f(x) .

Since $f(x)=4x^{2}+x-11$ here, we can use the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ to derive

$f'(x)=(2)4x^{2-1}+(1)x^{1-1}-(0)11=8x+1$ .

At the point (-2,5) , we have x=-2 , and so

f'(-2)=8(-2)+1=-16+1=-15 .

Report an Error

Example Question #107 : Derivatives

What is the slope of a function $f(x)=7x^{2}-2x+10$ at the point (-1,4) ?

Possible Answers:

None of the above

Correct answer:

Explanation:

By definition, slope is the first derivative of a given function f(x) .

Since $f(x)=7x^{2}-2x+10$ here, we can use the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ to derive

$f'(x)=(2)7x^{2-1}-(1)2x^{1-1}+(0)10=14x-2$ .

At the point (-1,4) , we have x=-1 , and so

f'(-1)=14(-1)-2=-14-2=-16 .

Report an Error

Example Question #21 : Derivative At A Point

Given a function $f(x)=9x^{2}-12x+20$ , what is its slope at the point (4,5) ?

Possible Answers:

Correct answer:

Explanation:

Slope is defined as the first derivative of a function at a given point.

Given

$f(x)=9x^{2}-12x+20$ . we can use the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ to derive

$f'(x)=(2)9x^{2-1}-(1)12x^{(1-1)}+(0)20=18x-12$ .

Since the -coordinate of (4,5) is , the slope

f'(4)=18(4)-12=72-12=60 .

Report an Error

Example Question #21 : Derivative At A Point

Given a function $f(x)=-3x^{2}+14x-23$ , what is its slope at the point (-2,-2) ?

Possible Answers:

Correct answer:

Explanation:

Slope is defined as the first derivative of a function at a given point.

Given

$f(x)=-3x^{2}+14x-23$ . we can use the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ to derive

$f'(x)=-3(2)x^{2-1}+(1)14x^{1-1}-(0)23=-6x+14$ .

Since the -coordinate of (-2,-2) is , the slope

f'(-2)=-6(-2)+14=12+14=26 .

Report an Error

Example Question #110 : Derivatives

Given a function $f(x)=\frac{1}{x^{2}}-3x+2$ , what is its slope at the point (4,1) ?

Possible Answers:

$\frac{32}{97}$

$-\frac{32}{97}$

$\frac{97}{32}$

None of the above.

$-\frac{97}{32}$

Correct answer:

$-\frac{97}{32}$

Explanation:

Slope is defined as the first derivative of a function at a given point. Given $f(x)=\frac{1}{x^{2}}-3x+2$ or $f(x)=x^{-2}-3x+2$ . we can use the Power Rule ( $\frac{d}{dx}x^{n}=nx^{n-1}$ for all $n\neq0$ ) to derive $f'(x)=(-2))x^{-2-1}-(1)3x^{1-1}+(0)2=-2x^{-3}-3=-\frac{2}{x^{3}}-3$ . Since the -coordinate of (4,1) is , the slope $f'(4)=-\frac{2}{4^{3}}-3=-\frac{2}{64}-3=-\frac{1}{32}-3=-\frac{1}{32}-\frac{96}{32}=-\frac{97}{32}$ .

Report an Error

Example Question #21 : Derivative At A Point

Find the derivative of $y=\left | x-3\right |$ at x=3 .

Possible Answers:

$\pm1$

Does not exist.

Correct answer:

Does not exist.

Explanation:

Split the absolute value into both positive and negative components.

$y=\left | x-3\right | = \pm(x-3)$

Take their derivatives.

$\frac{d}{dx}[y=x-3]=1$

$\frac{d}{dx}[y=-(x-3)]=-1$

At x=3 , there exists a spike in the graph. For spikes, the derivative does not exist under this exception.

The answer is:

$\textup{Does not exist.}$

Report an Error

Example Question #22 : Derivative At A Point

What is the slope of a function $f(x)=10x^{2}-25x+12$ at the point (5,7) ?

Possible Answers:

100

Correct answer:

Explanation:

Slope is defined as the first derivative of a function at given point.

We are given the function

$f(x)=10x^{2}-25x+12$ and a point (5,7) , so we need to find the derivative f'(x) and solve for the point's -coordinate.

Using the Power Rule

$\frac{d}{dx}x^{n}=nx^{n-1}$ for all nonzero , we can derive

$f'(x)=(2)10x^{2-1}-(1)25x^{1-1}+(0)12=20x-25$ .

Substituting the -coordinate , we have a slope:

f'(5)=20(5)-25=100-25=75 .

Report an Error

← Previous 1 2 3 4 5 6 7 8 9 10 11 12 Next →

View Calculus 2 Tutors

Gary
Certified Tutor

SUNY at Albany, Bachelor of Science, Economics. Pace University-New York, Masters in Business Administration, Analysis and Fu...

View Calculus 2 Tutors

Yoonsik
Certified Tutor

Seoul National University, Bachelor of Science, Physics. University of Pennsylvania, Doctor of Philosophy, Atomic and Molecul...

View Calculus 2 Tutors

Kurosh
Certified Tutor

University of tehran, Bachelor of Engineering, Electrical Engineering.

All Calculus 2 Resources

9 Diagnostic Tests 308 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

Chemistry Tutors in Boston, LSAT Tutors in Houston, LSAT Tutors in Philadelphia, English Tutors in Miami, Computer Science Tutors in Miami, Physics Tutors in Houston, Algebra Tutors in Boston, French Tutors in Miami, Algebra Tutors in New York City, English Tutors in Chicago

Popular Courses & Classes

GRE Courses & Classes in Los Angeles, Spanish Courses & Classes in New York City, LSAT Courses & Classes in San Francisco-Bay Area, SAT Courses & Classes in Seattle, LSAT Courses & Classes in Boston, ACT Courses & Classes in San Diego, SAT Courses & Classes in San Francisco-Bay Area, ACT Courses & Classes in Boston, MCAT Courses & Classes in Chicago, GRE Courses & Classes in Seattle

Popular Test Prep

ACT Test Prep in Boston, MCAT Test Prep in Phoenix, SSAT Test Prep in Boston, ISEE Test Prep in Washington DC, SAT Test Prep in New York City, ACT Test Prep in San Diego, ACT Test Prep in Chicago, SAT Test Prep in San Diego, GRE Test Prep in Los Angeles, ACT Test Prep in Phoenix

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 2 : Derivative at a Point

Study concepts, example questions & explanations for Calculus 2

All Calculus 2 Resources

Example Questions

Example Question #103 : Derivatives

Example Question #104 : Derivatives

Example Question #105 : Derivatives

Example Question #106 : Derivatives

Example Question #107 : Derivatives

Example Question #21 : Derivative At A Point

Example Question #21 : Derivative At A Point

Example Question #110 : Derivatives

Example Question #21 : Derivative At A Point

Example Question #22 : Derivative At A Point

All Calculus 2 Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: