# Tagged Questions

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### Minimum of a function $f(x,y)=\frac{(1+2y)(1+\frac{x}{2})}{(1+y)(1+x)+x}$

what is the minimum of a function \begin{align} f(x,y)&=\frac{(1+2y)(1+\frac{x}{2})}{(1+y)(1+x)+x}\\ \text {s.t. }& 1 \le y \le x \le y(1+y) \end{align} I asked Wolfram and Alfa and it says ...
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### Having a bit of trouble with min/max distance from sphere to point

The sphere is $x^2 + y^2 + z^2 = 81$ and the point is $(5,6,9)$ I am using Langrane multipliers , but the answers I am getting are so far off. I will post my system of equations soon. I found ...
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### How to find the absolute extrema of a function on an elliptical cylinder using Lagrange multipliers?

Optimize the function $f(x,y) = x^2y$ on the elliptical cylinder $\ x^2 \ + \ 2y^2 \ \le \ 6 \$ using Lagrange Multipliers. Well, from what I know that I have to find the gradient then to ...
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### Maximizing Area of Triangle in Circle

I was playing around with another example that I made up where I am trying to maximize the area of a triangle inscribed in a circle of radius. I want to do the problem using the method of Lagrange ...
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### Extrema of two variable function

Find extrema of $f(x,y)=x^2-xy+y^2$ from set $M=\{ [x,y] \in \mathbb{R}^2;|x|+|y|\le1\}$ I am solving this kind of problems for the first time and I am not sure what I am doing, what I have got ...
Two people, A and B, with respective utility functions of: $$U_a(X_a,Y_a) = X_a^2 Y_a\\ U_b(X_b,Y_b) = X_b Y_b^2$$ Total $X$ (that is, $X_a+X_b$) is fixed at $36$. Total $Y$ ($Y_a+Y_b$) is fixed ...