Linked Questions

13 votes
9 answers
5k views

Finding maximum or minimum of implicit functions

is there any built in function that can be used to find maximum or minimum of implicit functions? For example, if we have the equation $$x^2 + y^2 = (2 x^2 + 2 y^2 - x)^2,$$ then we can visualize the ...
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15 votes
3 answers
7k views

Finding all maxima and minima of a function

To find all (global and local) extrema of a function in $\mathbb R^3$, I have written the following. Example function: ...
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  • 34.6k
13 votes
1 answer
3k views

Lagrange Multiplier

We are asked to maximize and minimize $f(x,y)=4xy$, given the constraint $4x^2+y^2=8$, using the Lagrange Multiplier method. First, I enter the functions f and g. ...
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  • 14.6k
-1 votes
3 answers
7k views

How do I determine the maximum value for a polynomial, given a range of x values?

I need to determine the maximum value for y = a x^2 + b x + c, where I know the coefficients and the upper and lower x values. ...
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  • 99
8 votes
1 answer
996 views

Need help with the Lagrange multiplier method

Well I am new to Mathematica and got really stuck solving this problem. In class, I was ask to use the Lagrange multiplier method to find the maximum and minimum value of $f(x,y) = x^2+y^2$ which ...
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4 votes
1 answer
2k views

How do I get all possible solutions in an underdetermined system? [duplicate]

I have two problems which I'd like to solve with Mathematica. If I have a system of two equations with three unknowns, how can I get to list all possible solutions for the unknowns? Here is what I ...
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1 vote
1 answer
2k views

Symbolic Constrained Optimization

I have a question regarding evaluating constrained optimization problems in symbolic terms. I would like to perform How can I implement the method of Lagrange multipliers to find constrained extrema? ...
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  • 11
2 votes
4 answers
437 views

Using Lagrange multipliers to minimize function of six variables and an inequality

I want to form the function h = f − λ1 g1 − λ2 g2 − λ3 g3 − λ4 g4 where f is the function to minimize subject to the ...
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2 votes
1 answer
243 views

Maximize a variable in NSolve Function

I want to solve a set of trigometric coupled equations with the NSolve funcion while at the same time trying to maximize a variable which has to be real and between ...
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  • 121
2 votes
3 answers
229 views

Solve / brute-force for parameters that drive a function to zero at specified points

Edit: Made question a lot easier to read. Simple example. - Consider $p(x,y,z,t) = e^t(ax^2 + by^2 + cz^2)$ and I seek the values of $a,b,c$ which make $p\approx0$ at the point $(x=r\cos\theta,y=r\...
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  • 139
1 vote
1 answer
219 views

What methods does Maximize use like $\mathtt{Maximize}\left[\left\{3 x^2+2 \sqrt{2} x y,x^4+y^4=1\right\},\{x,y\}\right]$

I used Maximize for the maximum value of $3 x^2+2 \sqrt{2} x y$ when $x^4+y^4=1$ , $x>0,y>0$. What methods does Maximize ...
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  • 5,105
1 vote
0 answers
514 views

How can I calculate Lagrange multiplier and the critical points with Mathematica? [closed]

I have constraints and a function I want to know the critic points but is there a way that I can compute this method so that I can see results faster
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  • 11
2 votes
1 answer
224 views

Symbolic Non-Linear Maximization using Lagrangian

I am trying to solve a constrained optimisation problem using Lagrangian Multipliers. The particular case is standard microeconomic problem of a firm maximizing profits, which I want to extend once I ...
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1 vote
2 answers
96 views

Augmented function of function

I have two generic functions : ucdu[x : {__}] := Times @@ (x) and cb[x : {__}, p : {__}] := Plus @@ (x p) For instance, ...
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