In Problem use Theorem 2 to find the local extrema. f(x, y) = 4x 2 - xy
Question:
In Problem use Theorem 2 to find the local extrema.
f(x, y) = 4x2 - xy + y2 + 12
Transcribed Image Text:
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 critical point] 3. All second-order partial derivatives of fexist in some circular region containing (a, b) as center. 4. A = fa (a, b), B = fy (a, b), C = fyy(a, b) Then B² > 0 and A < 0, then f(a, b) is a local maximum. Case 2. If AC - B² > 0 and A > 0, then f(a, b) is a local minimum. Case 3. If AC B² < 0, then f has a saddle point at (a, b). Case 1. 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: 63% (11 reviews)
fx y 4x xy y 12 fxy8xy0 1 xyx 2y 0 2 Solving ...View the full answer
Answered By
Aun Ali
I am an Associate Member of Cost and Management Accountants of Pakistan with vast experience in the field of accounting and finance, including more than 17 years of teaching experience at university level. I have been teaching at both undergraduate and post graduate levels. My area of specialization is cost and management accounting but I have taught various subjects related to accounting and finance.
5.00+
13+ Reviews
32+ 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) = 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...
-
Use Theorem 2 to find local extrema in Problems 5-24. f(x,y) = x2 - y2 + 2x + 6y - 4
-
Use Theorem 2 to find local extrema in Problems 5-24. f(x,y) = - x2 + xy - 2y2 + x + 10y -5
-
According to the Mortgage Bankers Association, 10% of all home mortgage loans in California were in foreclosure in the fourth quarter of 2011. Assuming this rate holds, if you randomly pick 30...
-
Accounting goodwill is measured and identified as the difference between the amount paid for a firm and the net fair value of the assets and liabilities acquired. This accounting goodwill is an...
-
In each set of the measurements, find the measurement that is (a) The most accurate (b) The most precise. 1. 15.7 in.; 0.018 in.; 0.07 in. 2. 368 ft; 600 ft; 180 ft 3. 0.734 cm; 0.65 cm; 16.01 cm 4....
-
Consider the fuel consumption data in Table B.18. For the purposes of this exercise, ignore regressor $x_{1}$. Perform a thorough residual analysis of these data. What conclusions do you draw from...
-
The company reported the following balance sheet information: Total income tax expense for 2008 was $40,000. Compute the amount of cash paid for income taxes in2008. 2008 2007 Income taxes payable...
-
what is the risk premium for a stock when the risk free rate is 5%, the S&P 500 index has an expected return of 22% and the stock has a beta of 2.5?
-
Amiel Company reported sales revenue of $20.3 million and expenses of $11.1 million in 20X1, excluding the results of its 80%-owned subsidiary, Talia Company. Talia had $7.0 million of sales revenue...
-
In Problem use the description of the region R to evaluate the indicated integral. (x + y 2) dA; R R = {(x, y)|0 < xs y + 2, 0 < y s 1}
-
Use the method of Lagrange multipliers in Problem. Maximize and minimize f(x, y, z) = x + 10y + 2z subject to x 2 + y 2 + z 2 = 105
-
A certain raw material is classified as to moisture content X (in percent) and impurity Y (in percent). Let X and Y have the joint pmf given by (a) Find the marginal pmfs, the means, and the...
-
Contrast an offense that requires proof of causation with one that does not.
-
Given the fact that there are millions of Internet users throughout the United States, is it appropriate for courts to apply the contemporary community standards test in making determinations...
-
Has the moral integrity of the criminal law been jeopardized by the increasing number of offenses for which a person can be convicted without proof of any criminal intent?
-
Is there a justification for the criminal law not punishing a person for failing to act when there is a clear moral duty to act?
-
Should it be a defense to a charge of attempt that the accused voluntarily abandoned the attempt?
-
The intensity of the sunlight that reaches Earth's upper atmosphere is approximately 1400 W/m2. (a) What is the average energy density? (b) Find the rms values of the electric and magnetic fields.
-
What are the six activities involved in the physical supply/distribution system?
-
Explain why confidence levels are usually large, such as 0.95 or 0.99, but not extremely large, such as 0.999999.
-
For the observations 618, 650, 608, 634, 675, 618, 625, 619, 630 on Buy It Now prices for the iPhone 5s on eBay considered in Exercise 8.35, a confidence interval for the population mean Buy It Now...
-
Increasing the confidence level causes the margin of error of a confidence interval to a. Increase, b. Decrease, c. Stay the same.
-
Determine your monthly payment if you buy a $300,000 house at 6% with 15% down and pay it off over 30 years.
-
Revenue Recognition at a Point in Time versus Revenue Recognition Over Time. The market company won a contract to build a shopping center at a price of $300 million. The following schedule details...
-
Calculate the flat monthly instalment for the car loan amount of $450,000 over two years at 5% compounded semiannualy. You can use either geometric progression or an optimizer (Goal seek or Solver)...
Study smarter with the SolutionInn App