In Problem use Theorem 2 to find the local extrema. f(x, y) = e xy THEOREM 2
Question:
In Problem use Theorem 2 to find the local extrema.
f(x, y) = exy
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: 60% (10 reviews)
fx y exy Differentiating fxy with respect to x fxxyyexy Again differentia...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...
-
a) What would be the third term? What would be the next to last term? What would be the last term? b) What would be the second term? What would be the next to last term? What would be the last term?...
-
Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum with continuous compounding respectively. Estimate the cash price of a bond...
-
Calculate the energy destruction associated with each of the processes of the Brayton cycle described in Problem 973, assuming a source temperature of 1600 K and a sink temperature of 290 K.
-
What is meant by user-oriented systems design?
-
Absalom Motorss 14% coupon rate, semiannual payment, $1,000 par value bonds that mature in 30 years are callable 5 years from now at a price of $1,050. The bonds sell at a price of $1,353.54, and the...
-
What determines whether a company can pay its bills on time? Question 13 options: a) High employee morale b) Ability to reduce expenses easily c) Talent of its sales force d) Adequate cash flow
-
Who are the stakeholders in the corporation?
-
In Problem find the indicated value. f x (4, 1) if f(x, y) = x 2 y 2 - 5xy 3
-
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. : J R y = x + 1, y = 0, x =...
-
Why is it important to check your online persona?
-
The average distance between Earth and the Sun is 1.5 10 m. 1) Calculate the average speed of Earth in its orbit (assumed to be circular) in meters per second. 2) What is this speed in miles per hour?
-
The company would like to incorporate into the analysis its second major mixed nut line, the Hovel line. The Hovel mix can contain no more than 60 percent peanuts and no less than 20 percent almonds....
-
you surely know the tale of the 3 little pigs and the big bad wolf. Which of the three little piggies picked the best insulator for their building and why? The one who built with straw, wood or brick?
-
No matter how many times you do a Google search for online colleges, the first two returns are the University of Phoenix and Kaplan University. What does this fact tell you? That these two making use...
-
You own a grocery store chain that, among other things, sells bread to customers. You outsource the production of your bread to a bread manufacturing business (supplier) and want to assess the value...
-
Sally Cook, Lin Jing, and Ken Schwartz formed the CJS Partnership by making capital contributions of $144,000, $216,000, and $120,000, respectively. They predict annual partnership net income of...
-
Write a program to move a signed number from smaller register to bigger register. Hint: movzx ax, bl Topic: Data Related Operators and Directives in assembly language
-
Given a standard normal distribution, find the area under the curve that lies (a) To the left of z = 1.39; (b) To the right of z = 1.96; (c) Between z = 2.16 and z = 0.65; (d) To the left of z =...
-
Suppose X follows a continuous uniform distribution from 1 to 5. Determine the conditional probability P(X > 2.5 | X 4).
-
Given a continuous uniform distribution, show that (a) = A + B/2 and (b) 2 = (B A) 2 /12 .
-
A stock's dividend in 1 year is expected to be $2.57. The dividend amount per year is expected to remain the same indefinitely. The stock's required return is 11%. The estimated value of the stock...
-
Jare Asset valuation and risk Personal Finance Problem Laura Drake wishes to estimate the value of an asset expected to provide cash inflows of $2,200 for each of the next 4 years and $10,859 in 5...
-
You just won the lottery and have elected to receive it in equal payments, starting today and lasting 20 years (20 payments). The value of the lottery is $2,500,000 today. If the lottery's discount...
Study smarter with the SolutionInn App