New User Special Price Expires in

Let's log you in.

Sign in with Facebook


Don't have a StudySoup account? Create one here!


Create a StudySoup account

Be part of our community, it's free to join!

Sign up with Facebook


Create your account
By creating an account you agree to StudySoup's terms and conditions and privacy policy

Already have a StudySoup account? Login here

Tangent Planes, Normal Lines, Extrema and Lagrange Multipliers

by: Saul Cervantes

Tangent Planes, Normal Lines, Extrema and Lagrange Multipliers Math 2419

Marketplace > University of Texas at Dallas > Mathematics (M) > Math 2419 > Tangent Planes Normal Lines Extrema and Lagrange Multipliers
Saul Cervantes
Accelerated Calculus II
Anotoly Ezlydon

Almost Ready


These notes were just uploaded, and will be ready to view shortly.

Purchase these notes here, or revisit this page.

Either way, we'll remind you when they're ready :)

Preview These Notes for FREE

Get a free preview of these Notes, just enter your email below.

Unlock Preview
Unlock Preview

Preview these materials now for free

Why put in your email? Get access to more of this material and other relevant free materials for your school

View Preview

About this Document

Accelerated Calculus II
Anotoly Ezlydon
Class Notes
25 ?




Popular in Accelerated Calculus II

Popular in Mathematics (M)

This 6 page Class Notes was uploaded by Saul Cervantes on Tuesday October 20, 2015. The Class Notes belongs to Math 2419 at University of Texas at Dallas taught by Anotoly Ezlydon in Fall 2015. Since its upload, it has received 20 views. For similar materials see Accelerated Calculus II in Mathematics (M) at University of Texas at Dallas.


Reviews for Tangent Planes, Normal Lines, Extrema and Lagrange Multipliers


Report this Material


What is Karma?


Karma is the currency of StudySoup.

You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/20/15
TANGENT PLANES NORMAL LINES EXTREMA AND LAGRANGE MULTIPLIERS 0 Let FX y 2 be differentiable at AX0 yo zo Suppose that VF at 0 o The plane through A that is normal to VF x0 y0 20 is called the tangent plane 0 The line through A that is perpendicular to the tangent plane is called the normal line Angle of Inclination Angle between tangent plane and the xyplane Vector normal to the tangent plane is Vf Vector normal to the xyplane islt0 0 1gt 39k To nd angle of 1nc11natlon C059 Extrema of Function of Two Variables 0 Critical Points are candidates for extrema 0 Critical points exist Where V f lt 0 0 0 gt or Vf does not exist Second Derivative Test 1 fxxfyy fxy2 If 1 gt 0 and fxxa b gt 0 then f has a relative minimum at the point a b If 1 gt 0 and fxxa b lt 0 then f has a relative maximum at the point a b If 1 lt 0 then point a b fa b is a saddle point If 1 0 the test is inconclusive OOOO Qgrange Multipliers If f and g are differentiable then VfAVg gtgc fxAgx fyAgy Evaluate f at each solution obtained from the above equations The greatest value yields the maximum of f subject to the constraint gX y c and the least value yields the minimum of f subject to the constraint gX y c


Buy Material

Are you sure you want to buy this material for

25 Karma

Buy Material

BOOM! Enjoy Your Free Notes!

We've added these Notes to your profile, click here to view them now.


You're already Subscribed!

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

Why people love StudySoup

Jim McGreen Ohio University

"Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Jennifer McGill UCSF Med School

"Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over $500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Steve Martinelli UC Los Angeles

"There's no way I would have passed my Organic Chemistry class this semester without the notes and study guides I got from StudySoup."

Parker Thompson 500 Startups

"It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!

Refund Policy


All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email


StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here:

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to

Satisfaction Guarantee: If you’re not satisfied with your subscription, you can contact us for further help. Contact must be made within 3 business days of your subscription purchase and your refund request will be subject for review.

Please Note: Refunds can never be provided more than 30 days after the initial purchase date regardless of your activity on the site.