In Problem use Theorem 2 to find the local extrema. f(x, y) = 2x 4 + y
Question:
In Problem use Theorem 2 to find the local extrema.
f(x, y) = 2x4 + y2 - 12xy
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: 75% (12 reviews)
The first st...View the full answer
Answered By
Utsab mitra
I have the expertise to deliver these subjects to college and higher-level students. The services would involve only solving assignments, homework help, and others.
I have experience in delivering these subjects for the last 6 years on a freelancing basis in different companies around the globe. I am CMA certified and CGMA UK. I have professional experience of 18 years in the industry involved in the manufacturing company and IT implementation experience of over 12 years.
I have delivered this help to students effortlessly, which is essential to give the students a good grade in their studies.
3.50+
2+ 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...
-
Suppose the graph represents the sales of goods of a company from the year 2000 to 2008. a) Find the average rate of change from x = 1 to x = 4 and interpret. b) Find the average rate of change from...
-
The cash prices of six-month and one-year Treasury bills are 94.0 and 89.0. A 1.5-year bond that will pay coupons of $4 every six months currently sells for $94.84. A two-year bond that will pay...
-
What does the Bible teach about God in these accounts?
-
Eighteen plots of land in Indiana were given different applications of nitrogen. In each case, the previous crop had been soybeans and all other factors were roughly comparable. Use the 18...
-
Refer to the data in Exercise, regarding Saskatewan Can Company. Prepare journal entries to: Saskatewan Can Company manufactures recyclable soft-drink cans. A unit of production is a case of 12 dozen...
-
Simon Company's year-end balance sheets follow. At December 31 Assets Current Year 1 Year Ago 2 Years Ago Cash $ 30,162 Accounts receivable, net Merchandise inventory Prepaid expenses Plant assets,...
-
Consider two Italian restaurants located in identical towns 200 miles apart. The restaurants are identical in every respect but their tipping policies. At one, there is a flat $15 service charge, but...
-
Data on U.S. property crimes (in number of crimes per 100,000 population) are given in the table for the years 2001 through 2015. (A) Find the least squares line for the data, using x = 0 for 2000....
-
In Problem graph the region R bounded by the graphs of the indicated equations. Describe R in set notation with double inequalities, and evaluate the indicated integral. y = 1 - x, y = 1 + x, x = 4;...
-
During 2015, Callaway Company disposed of three different assets. On January 1, 2015, prior to the disposal of the assets, the accounts reflected the following: The machines were disposed of in the...
-
If the marginal product of labor is 2 units of output per day per worker for the first five workers and 0 units of output for the sixth worker onward, draw the total product curve, the average...
-
Using a graph similar to Figure 12.7, explain why a firm might not want to spend \(A\) on advertising, even though it shifts the firm's demand curve to the right. Figure 12.7:- p. $ per unit P2 P B...
-
Suppose that the cost function curve for a natural monopoly is \(C(Q)=48+6 Q\) and the inverse demand function it faces is \(p=38-2 Q\). What are the firm's maximum profits if it cannot price...
-
The Big Mac index was created by The Economist in 1986 as a lighthearted guide to whether currencies are at their correct level. The file BigMacIndex201807 contains the dollar price (rounded to two...
-
Moore Manufacturing Pty Ltd makes refrigerators and is trying to determine the cost of its ending work in process. The accountant has put together the following data for the year ended 30 June 2019....
-
A parallel plate capacitor is attached to a battery that supplies a constant voltage. While the battery remains attached to the capacitor the distance between the parallel plates increases by 25%....
-
1A. If the researcher is concerned about the number of variables, the nature of the analysis, and completion rates, then, he/she is at which stage of the sampling design process (Figure 11.1 in the...
-
A public health nurse has conducted a survey of people in the community to better comprehend the effectiveness of the flu shot this season using the following survey instrument: Flu Survey 1. Gender:...
-
A public health nurse has conducted a survey of people in the community to better comprehend the effectiveness of the flu shot this season using the following survey instrument: Flu Survey 1. Gender:...
-
The Acme Industries Safety Supervisor wants to determine the factors that predict employees passing the annual required site safety competency training course. Data set: Ch 12 Exercise 10B.sav...
-
Problem: Module 3 Textbook Problem 5 Learning Objective: 3-6 Using the straight-line method show how bonds issued at a discount. affect financial statements Diaz Company issued $91,000 face value of...
-
Manvir had to make payments of $1,125 every 6 months to settle a $22,000 loan that he received at 4.52% compounded semi-annually. a. How long did it take to settle the loan?
-
If I invest a single amount of $14,000 in an account earning 8% p.a. compounding quarterly for 5 years, how much interest will I have earned in those 5 years?
Study smarter with the SolutionInn App