In Problem use Theorem 2 to find the local extrema. f(x, y) = -x 2 + 2xy
Question:
In Problem use Theorem 2 to find the local extrema.
f(x, y) = -x2 + 2xy - 2y2 - 20x + 34y + 40
Transcribed Image Text:
THEOREM 2 Second-Derivative Test for Local Extrema If 1. z = f(x, y) 2. fx(a, b) = 0 and f(a, b) = 0 [(a, b) is a critical point] 3. All second-order partial derivatives of fexist in some circular region containing (a, b) as center. 4. A = f(a, b), B = fxy(a, b), C = fyy(a, b) Then Case 1. If AC - - Case 2. If AC - B² > 0 and A < 0, then f(a, b) is a local maximum. B² 0 and A > 0, then f(a, b) is a local minimum. B² < 0, then fhas a saddle point at (a, b). Case 3. If AC = Case 4. If AC - B² = 0, the test fails.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 61% (13 reviews)
fx y x 2 2xy 2y 2 20x 34y 40 Differentiating fxy with respect to x f...View the full answer
Answered By
Sahin Alam
As a tutor I always want such students and such opportunities where I can use my knowledge and experience. As I have ability to work hard and I use this tool by providing students solutions with easy methods. So that students can understand very easily and learn logics of mathematics. As I have graduated in Mathematics and I have a lot experience about teaching students. And I think this experience help me a
0.00
0 Reviews
10+ Question Solved
Related Book For
College Mathematics For Business Economics, Life Sciences, And Social Sciences
ISBN: 978-0134674148
14th Edition
Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker
Question Posted:
Students also viewed these Mathematics questions
-
In Problem use Theorem 2 to find the local extrema. f(x, y) = 4x 2 - xy + y 2 + 12 THEOREM 2 Second-Derivative Test for Local Extrema If 1. z = f(x, y) 2. f(a, b) = 0 and f,(a, b) = 0[(a, b) is a...
-
In Problem use Theorem 2 to find the local extrema. f(x, y) = x 2 + 3xy + 2y 2 + 5 THEOREM 2 Second-Derivative Test for Local Extrema If 1. z = f(x, y) 2. f(a, b) = 0 and f,(a, b) = 0[(a, b) is a...
-
In Problem use Theorem 2 to find the local extrema. f(x, y) = y ln x + 3xy THEOREM 2 Second-Derivative Test for Local Extrema If 1. z = f(x, y) 2. fx(a, b) = 0 and f(a, b) = 0 [(a, b) is a critical...
-
Which of the following is not an example of supervised machine learning? O Clustering O Deep learning O Decision Tree Linear Regression
-
A trader owns 55,000 units of a particular asset and decides to hedge the value of her position with futures contracts on another related asset. Each futures contract is on 5,000 units. The spot...
-
Jerry bicycles from his dorm to the local fitness center: 3.00 miles east and 2.00 miles north. Cindy's apartment is located 1.50 miles west of Jerry's dorm. If Cindy is able to meet Jerry at the...
-
Natural frequency of aluminum bar given by consistent-mass matrices a. \(58554 \mathrm{rad} / \mathrm{s}\) lumped-mass matrices b. \(33806 \mathrm{rad} / \mathrm{s}\) consistent-mass matrices c....
-
Mount Prospect Nursery School Company provides baby-sitting and child-care programs. On January 31, 2014, the company had the following trial balance: During the month of February, the company...
-
Graph what happens in the Newhouse model if originally everyone is uninsured, and then everyone is covered under a national health insurance plan with a co-insurance rate. (Don't worry about the size...
-
A lease agreement that qualifies as a finance lease calls for annual lease payments of $50,000 over a four-year lease term (also the asset's useful life), with the first payment at January 1, the...
-
A company produces x units of product A and y units of product B (both in hundreds per month). The monthly profit equation (in thousands of dollars) is given by P(x, y) = -4x 2 + 4xy - 3y 2 + 4x +...
-
In Problem evaluate each iterated integral. See Problem 15 [S 3yex+y dx dy 0 0
-
Explain what the term mutual agency means in regard to a partnership.
-
Blair, CPA, uses the cash receipts and disbursements method of reporting. In Year 7, a client gave Blair 100 shares of a listed corporation's stock in full satisfaction of a $5,000 accounting fee the...
-
How does financial forecasting contribute to strategic decision-making for businesses?In the context of personal financial planning, what role does tax planning play?
-
Wha is the value of the rate of interest that doubles your initial deposit of compound interest compounded continuously in 6 years?
-
With regards to worldwide monetary administration for a situation study, what are openings, and how would they influence an organization's monetary security and dynamic in the worldwide market?
-
What effect would a wildfire that burned so hot that it sterilized the soil, killing all the microbes, have on the nitrogen cycle?
-
You would like to own a common stock that has a record date of Friday, September 6, 2013. What is the last date that you can purchase the stock and still receive the dividend?
-
On October 1, 2021, Adoll Company acquired 2,600 shares of its $1 par value stock for $38 per share and held these shares in treasury. On March 1, 2023, Adoll resold all the treasury shares for $34...
-
The characteristics measured by a researcher are called ____.
-
The objects being studied by a researcher are called ____.
-
In a correlational design, the two variables are simply measured; they are not ____ by the experimenter.
-
Assume you have a portfolio consisting of a $400,000 investment in stock A and a $600,000 investment in stock B. Suppose that the daily volatilities of these two assets are 2% and 1.5%, respectively,...
-
Larkspur Company sells discounted shoes to the fashion-oriented consumer. The following schedule relates to the company's inventory for the month of March: Cost Sales March 1 Beginning inventory...
-
What is the role of education in promoting social mobility and reducing inequality, and how can educational systems be reformed to better serve diverse populations while preparing individuals for the...
Study smarter with the SolutionInn App