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### 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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### 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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### 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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### 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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### 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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### 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 ...
1 vote
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### 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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### 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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### 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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1 vote
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### 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