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

Example Question #31 : Derivative At A Point

What is the slope of a function $f(x)=x^{2}+7x-3$ at the point (-3,0) ?

Possible Answers:

$\frac{1}{3}$

None of the above

Correct answer:

Explanation:

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

We are given the function

$f(x)=x^{2}+7x-3$ and a point (-3,0) , 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

$f'(x)=(2)x^{2-1}+(1)7x^{1-1}-(0)3=2x+7$ .

Substituting the -coordinate , we have a slope:

f'(-3)=2(-3)+7=-6+7=1 .

Report an Error

Example Question #111 : Derivatives

What is the slope of a function $f(x)=6x^{2}-12x+9$ at the point (-10,10) ?

Possible Answers:

132

None of the above

Correct answer:

Explanation:

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

We are given the function

$f(x)=6x^{2}-12x+9$ and a point (-10,10) , 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

$f'(x)=(2)6x^{2-1}-(1)12x^{1-1}+(0)9=12x-12$ .

Substituting the -coordinate , we have a slope:

f'(-10)=12(-10)-12=-120-12=-132 .

Report an Error

Example Question #112 : Derivatives

What is the slope of $f(x)=4x^{2}-5x+12$ at (1,-1) ?

Possible Answers:

Correct answer:

Explanation:

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

Since,

$f(x)=4x^{2}-5x+12$ , we can use the Power Rule

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

$f'(x)=(2)4x^{2-1}-(1)5x^{1-1}+(0)12=8x-5$ .

At the point (1,-1) , the -coordinate is .

Thus, the slope is

f'(1)=8(1)-5=8-5=3 .

Report an Error

Example Question #111 : Derivatives

What is the slope of $f(x)=x^{2}+2x+11$ at (3,0) ?

Possible Answers:

Correct answer:

Explanation:

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

Since,

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

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

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

At the point (3,0) , the -coordinate is .

Thus, the slope is

f'(3)=2(3)+2=6+2=8 .

Report an Error

Example Question #114 : Derivatives

What is the slope of $f(x)=7x^{2}-6$ at (5,3) ?

Possible Answers:

Correct answer:

Explanation:

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

Since,

$f(x)=7x^{2}-6$ , we can use the Power Rule

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

$f'(x)=(2)7x^{1-1}-(0)6=14x$ .

At the point (5,3) , the -coordinate is .

Thus, the slope is f'(5)=14(5)=70 .

Report an Error

Example Question #1241 : Calculus Ii

What is the slope of a function f(x)=5x^2-x+7 at the point (4,5) ?

Possible Answers:

None of the above

Correct answer:

Explanation:

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

Since f(x)=5x^2-x+7 , we can use the Power Rule

$\frac{d}{dx}x^n=nx^{n-1}$ for all $n\neq 0$ to determine that

$f'(x)=(2)5x^{2-1}-(1)x^{1-1}+(0)7=10x-1.$

Since we're given a point (4,5) , we can use the -coordinate to solve for the slope at that point.

Thus,

f'(4)=10(4)-1=40-1=39 .

Report an Error

Example Question #13 : Derivative Defined As Limit Of Difference Quotient

What is the slope of a function f(x)=-2x^2+5x-3 at the point (0,1) ?

Possible Answers:

Correct answer:

Explanation:

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

Since f(x)=-2x^2+5x-3 , we can use the Power Rule

$\frac{d}{dx}x^n=nx^{n-1}$ for all $n\neq 0$ to determine that

$f'(x)=(2)(-2)x^{2-1}+(1)5x^{1-1}-(0)3=-4x+5$ .

Since we're given a point (0,1) , we can use the x-coordinate to solve for the slope at that point.

Thus,

f'(0)=-4(0)+5=5.

Report an Error

Example Question #116 : Derivatives

What is the slope of a function f(x)=-x^2+8x-4 at the point (-1,0) ?

Possible Answers:

$-\frac{1}{10}$

$\frac{1}{10}$

None of the above

Correct answer:

Explanation:

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

Since f(x)=-x^2+8x-4 , we can use the Power Rule

$\frac{d}{dx}x^n=nx^{n-1}$ for all $n\neq 0$ to determine that

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

Since we're given a point (-1,0) , we can use the x-coordinate to solve for the slope at that point.

Thus,

f'(-1)=-2(-1)+8=2+8=10 .

Report an Error

Example Question #1241 : Calculus Ii

What is the slope of the tangent line to the function

$h(x)=e^{x}ln(x)$

when x = 1?

Possible Answers:

$\frac{1}{e}$

Correct answer:

Explanation:

The slope of the tangent line to a function at a point is the value of the derivative at that point. To calculate the derivative in this problem, the product rule is necessary. Recall that the product rule states that:

$\frac{d}{dx}(m(x)n(x))=m'(x)n(x)+m(x)n'(x)$ .

In this example, $m(x)=e^x \ and\ n(x)=ln(x).$

Therefore,

$m'(x)=e^x \ and\ n'(x)=\frac{1}{x}$ , and

$\frac{d}{dx}(e^xln(x))=e^xln(x)+e^x\cdot\frac{1}{x}$

At x = 1, this dervative has the value

$e^1ln(1)+e^1\cdot\frac{1}{1}=0+e=e$ .

Report an Error

Example Question #32 : Derivative At A Point

Find the derivative of the following function at x=0 :

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

Possible Answers:

Correct answer:

Explanation:

The derivative of the function is

$f'(x)=-2\cos(x)\sin(x)+3$

and was found using the following rules:

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

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

$\frac{d}{dx}f(g(x))=f'(g(x))\cdot g'(x)$

where $f(x)=\cos^2(x), g(x)=x$ in the chain rule.

Plug in 0 in the derivative function to get f'(x)=3

Report an Error

View Calculus 2 Tutors

Max
Certified Tutor

SHAHiDBEHESHTiUNiVERSiTY, Bachelor of Science, Mathematics. SHAHiDBEHESHTiUNiVERSiTY, Master of Science, Mathematics.

View Calculus 2 Tutors

Juhyeon
Certified Tutor

Vanderbilt University, Master of Science, Environmental Engineering.

View Calculus 2 Tutors

Nevryk
Certified Tutor

University of Nevada-Las Vegas, Bachelor of Science, Computer Science.

All Calculus 2 Resources

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

Popular Subjects

Reading Tutors in Miami, ACT Tutors in Philadelphia, LSAT Tutors in Los Angeles, MCAT Tutors in Philadelphia, Computer Science Tutors in San Diego, Computer Science Tutors in Washington DC, Math Tutors in San Diego, Reading Tutors in New York City, ISEE Tutors in Washington DC, GRE Tutors in Atlanta

Popular Courses & Classes

MCAT Courses & Classes in San Diego, MCAT Courses & Classes in Houston, ISEE Courses & Classes in Denver, MCAT Courses & Classes in Dallas Fort Worth, ISEE Courses & Classes in Phoenix, ACT Courses & Classes in San Francisco-Bay Area, LSAT Courses & Classes in Los Angeles, GRE Courses & Classes in San Diego, MCAT Courses & Classes in Washington DC, LSAT Courses & Classes in Chicago

Popular Test Prep

ACT Test Prep in San Francisco-Bay Area, MCAT Test Prep in Washington DC, ISEE Test Prep in Los Angeles, SAT Test Prep in Dallas Fort Worth, GRE Test Prep in Atlanta, LSAT Test Prep in San Francisco-Bay Area, SSAT Test Prep in New York City, ACT Test Prep in Houston, ACT Test Prep in Boston, MCAT Test Prep in San Francisco-Bay Area

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 #31 : Derivative At A Point

Example Question #111 : Derivatives

Example Question #112 : Derivatives

Example Question #111 : Derivatives

Example Question #114 : Derivatives

Example Question #1241 : Calculus Ii

Example Question #13 : Derivative Defined As Limit Of Difference Quotient

Example Question #116 : Derivatives

Example Question #1241 : Calculus Ii

Example Question #32 : 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: