Call Now to Set Up Tutoring:

(888) 888-0446

Precalculus : Find the Slope of a Line Tangent to a Curve At a Given Point

Study concepts, example questions & explanations for Precalculus

Create An Account

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Find the slope of the line y=3x^3 at the point (1,3) .

Possible Answers:

m=1

m=3

m=9x^2

m=9

Correct answer:

m=9

Explanation:

First find the slope of the tangent to the line by taking the derivative.

Using the Exponential Rule we get the following,

y=3x^3

$\frac{dy}{dx}=9x^2$ .

Then plug 1 into the equation as 1 is the point to find the slope at.

$\frac{dy}{dx}=9(1)^2=9(1)=9$ .

Report an Error

Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Find the slope of the following expression at the point (2,3)

y=x^3+2x^2+x .

Possible Answers:

Correct answer:

Explanation:

One way of finding the slope at a given point is by finding the derivative. In this case, we can take the derivative of y with respect to x, and plug in the desired value for x.

y=x^3+2x^2+x

Using the exponential rule we get the following derivative,

$\frac{\mathrm{d}y }{\mathrm{d} x}=3x^2 +4x+1$ .

Plugging in x=2 from the point 2,3 gives us the final slope,

3(2)^2+4(2)+1

=3(4)+8+1

=12+9=21

Thus our slope at the specific point is .

Note that in this case, using the y coordinate was not necessary.

Report an Error

Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Find the slope of the tangent line of the function at the given value

f(x)=3x^2

x=3 .

Possible Answers:

Correct answer:

Explanation:

To find the slope of the tangent line of the function at the given value, evaluate the first derivative for the given.

The first derivative is

$f^{'}(x)=anx^{n-1}$

and for this function

$f^{'}(x)=3(2)x^{2-1}=6x$

and

f'(3)=6(3)=18

So the slope is

Report an Error

Example Question #2 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Find the slope of the tangent line of the function at the given value

f(x)=x^2+4x

x=1 .

Possible Answers:

Correct answer:

Explanation:

To find the slope of the tangent line of the function at the given value, evaluate the first derivative for the given value.

The first derivative is

$f^{'}(x)=anx^{n-1}$

and for this function

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

and plugging in the specific x value we get,

f'(1)=2(1)+4=6

So the slope is

Report an Error

Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Consider the function y=2x^2+10x . What is the slope of the line tangent to the graph at the point (1,12) ?

Possible Answers:

Correct answer:

Explanation:

Calculate the derivative of y=2x^2+10x by using the derivative rules. The derivative function determines the slope at any point of the original function.

The derivative is: y'=4x+10

With the given point (1,12) , x=1 . Substitute this value to the derivative function to determine the slope at that point.

y'=4(1)+10=14

The slope of the tangent line that intersects point (1,12) is .

Report an Error

View Pre-Calculus Tutors

James
Certified Tutor

St. Mary of the Plains College, Bachelors, Mathematics. Baker University, Masters, Business Administration and Management.

View Pre-Calculus Tutors

Satweka
Certified Tutor

The University of Texas at Dallas, Master of Science, Biomedical Engineering.

View Pre-Calculus Tutors

Pankaj
Certified Tutor

University of Delhi, Electrical Engineer, Electrical Engineering. Columbia University in the City of New York, Master of Arts...

All Precalculus Resources

12 Diagnostic Tests 380 Practice Tests Question of the Day Flashcards Learn by Concept

Popular Subjects

GMAT Tutors in Phoenix, English Tutors in Seattle, GMAT Tutors in Chicago, Physics Tutors in Philadelphia, Chemistry Tutors in Dallas Fort Worth, GRE Tutors in Denver, Computer Science Tutors in Dallas Fort Worth, SAT Tutors in Phoenix, GRE Tutors in Seattle, Spanish Tutors in Seattle

Popular Courses & Classes

SAT Courses & Classes in Los Angeles, ISEE Courses & Classes in Miami, SAT Courses & Classes in Atlanta, GRE Courses & Classes in Los Angeles, GRE Courses & Classes in Houston, GMAT Courses & Classes in Phoenix, MCAT Courses & Classes in San Diego, SAT Courses & Classes in Washington DC, Spanish Courses & Classes in San Diego, ISEE Courses & Classes in Chicago

Popular Test Prep

GMAT Test Prep in Phoenix, LSAT Test Prep in Philadelphia, MCAT Test Prep in Houston, SAT Test Prep in Seattle, SAT Test Prep in San Diego, ACT Test Prep in Boston, SAT Test Prep in Washington DC, GRE Test Prep in Phoenix, ACT Test Prep in Phoenix, SAT Test Prep in Boston

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

Precalculus : Find the Slope of a Line Tangent to a Curve At a Given Point

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Example Question #2 : Find The Slope Of A Line Tangent To A Curve At A Given Point

Example Question #1 : Find The Slope Of A Line Tangent To A Curve At A Given Point

All Precalculus Resources

Report an issue with this question

DMCA Complaint

Contact Information

Address

Complaint Details

Email address:
Your name:
Feedback: