Find the absolute extrema of $f(x,y) = x^2 - xy + y^2$ on $|x| + |y| \leq 1$.
Hello. I am confused about how to solve the following Lagrange multiplier problem. It involves in inequality in the constraint so I began by finding the extrema within that domain by simply setting the first derivatives of f to 0, and finding that there is an extremum at (0, 0). However, the absolute values in the constraint confuse me when I try to use Lagrange multipliers. Can someone help me?
Find the absolute extrema of $f(x,y) = x^2 - xy + y^2$ on $|x| + |y| \leq 1$.
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
1 Attachment
Kav10
2.1K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 700 views
- $9.00
Related Questions
- Evaluate the integral $\int_{-\infty}^{+\infty}e^{-x^2}dx$
- Minimizing the cost of building a box
- In what direction the function $f(x,y)=e^{x-y}+\sin (x+y^2)$ grows fastest at point $(0,0)$?
- Analyzing the Domain and Range of the Function $f(x) = \frac{1}{1 - \sin x}$
- Rainbow Vectors
- Derivative of FUNCTION
- Evaluate$\int \sqrt{\tan x}dx$
- Find the arc length of $f(x)=x^{\frac{3}{2}}$ from $x=0$ to $x=1$.
