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### Find Maximum and Minimum distance from origin to $f(x,y)$ using the Lagrange method.

You've done fine to conclude that $x^2=y^2.$ That means $x=y$ or that $x=-y.$ Plug each of those into your curve's equation. You should find four distinct points of two distinct distances from the ...
• 103k
1 vote

### Find Maximum and Minimum distance from origin to $f(x,y)$ using the Lagrange method.

You need to plug $y = x$ and $y = -x$ into the equation and solve for $x$ and $y$ properly (you made a mistake when solving). Once you do that you will get $4$ possible solutions. Two will be at one ...
• 45k
1 vote

### Find Maximum and Minimum distance from origin to $f(x,y)$ using the Lagrange method.

Note that this method relies heavily on the AM-GM inequality,but you can connect it with your Lagrage Multiplier method to sort out the points that lie furthest from the origin. For the farthest, ...
• 6,538
1 vote

• 33.4k
1 vote

### Multivariable Calculus - Exercise about Lagrange multipliers

OP has derived these : \begin{align}y &= 2x\lambda \tag{EQ 1} \\ 2y+x &= 2y\lambda \tag{EQ 2} \\ 0 &= 2z\lambda \tag{EQ 3} \\ x^{2}+y^{2}+z^{2}-4&= 0 \tag{EQ 4} \end{align} With ...
• 9,819
1 vote

### Find the distance between tangent space and the origin

Let's assume $F(0)=0$. Let's also assume $\alpha\neq 0$, otherwise we can get arbitrarily close to the origin in $S$ by considering $F(ta)$ for arbitrarily small, positive $t$. Fix $0\neq a\in S$. As ...
• 2,057
1 vote

### Finding the extreme values of $f(x,y,z)=x^2+y^2+z^2$ constraint to $x^2+y^2+z^2+xy=12$

You can avoid any complicated inequalities or Lagrange multipliers by diagonalizing the constraint: $g(x,y,z) = x^2+xy+y^2+z^2$ can be written as $\frac{1}{4}(x-y)^2+\frac{3}{4}(x+y)^2+z^2$. Thus ...
• 4,558

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