In Problem use Theorem 2 to find the local extrema. f(x, y) = x 3 + y
Question:
In Problem use Theorem 2 to find the local extrema.
f(x, y) = x3 + y3 - 3xy
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: 37% (8 reviews)
fx y x 3 y 3 3xy first f x xy 0 3x 2 ...View the full answer
Answered By
Hardik Dudhat
I am semi-qualified Chemical Engineering ,I have scored centum in accounting in my senior secondary and in my graduation. I have always helped my fellow students with their concerns on the subject, i have tutored on various tutoring sites in the past and also have taken home tuitions for degree and MBA students. As a tutor, I don't want my students to just get a solution, I want them to understand the concept and never have a doubt in that area thereon and i believe in excelling and not in educating.
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...
-
Consider the following population regression model: y = Bo + Bx + Bx2 + 3x3 + u Suppose you want to test whether 0.532 = 83. The hypotheses are: Ho : 0.582 = 33 H : 0.532 #33 The correct expression...
-
When the zero curve is upward sloping, the zero rate for a particular maturity is greater than the par yield for that maturity. When the zero curve is downward sloping the reverse is true. Explain...
-
Explain the goals of financial analysis in detail.
-
How does an objects interface relate to services that the object provides?
-
City Publishing was recently organized. The company issued common stock to an attorney who provided legal services worth $17,000 to help organize the corporation. City Publishing also issued common...
-
InstaChat Company had a beginning retained earnings balance of $80,000 and an ending retained earnings balance of $60,000. In the current period the company had revenues of $110,000 and expenses of...
-
The highway police in a certain state are using aerial surveillance to control speeding on a highway with a posted speed limit of 55 miles per hour. Police officers watch cars from helicopters above...
-
In Problem find the indicated value. f y (2, 4) if f(x, y) = x 4 ln y
-
In Problem find the indicated value of the given function. A(100, 0.06, 3) for A(P, r, t) = P + Prt
-
Use the same facts as in Problem 31 except that Brandlin Company purchases materials from a foreign supplier on December 1, 2017, with payment of 16,000 korunas to be made on March 1, 2018. The...
-
Discuss how yields anticipate future economic activity.
-
List and explain the three components of a lecture.
-
Discuss the different methods of payment and the future of money.
-
Demonstrate how to reduce risk through hedging and diversification.
-
Municipal bonds are usually exempt from income taxes. Because investors care about the after-tax returns on their investments, these bonds have lower yields than bonds whose interest payments are...
-
Why are all parts of a conductor at the same potential in electrostatic equilibrium?
-
Which of the followingcarbocations is the least stable? CH3CH2 . CH3CHCH3 CH3 I . CH3C0 T CH3 IV. V. CH3 CH3CCH2 CH3
-
Compute 95% confidence intervals for the proportion of defective items in a process when it is found that a sample of size 100 yields 8 defectives.
-
Fortune magazine (March 1997) reported the total returns to investors for the 10 years prior to 1996 and also for 1996 for 431 companies. The total returns for 9 of the companies and the S&P 500 are...
-
The federal government awarded grants to the agricultural departments of 9 universities to test the yield capabilities of two new varieties of wheat. Each variety was planted on a plot of equal area...
-
s Machine-hours required to support estimated production Fixed manufacturing overhead cost Variable manufacturing overhead cost per machine-hour Required: 1. Compute the plantwide predetermined...
-
How do visionary leaders navigate the complexities of organizational dynamics to cultivate a culture of innovation and adaptability ? Explain
-
Finnish Corporation manufactures custom molds for use in the extrusion industry. The company allocates manufacturing overhead based on machine hours. Selected data for costs incurred for Job 532 are...
Study smarter with the SolutionInn App