# Questions tagged [maximum]

Questions on finding the largest value of a set, extreme values of an expression, or on Mathematica functionality for maxima testing.

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### Find the global maxima over the interval [0,1]

I am trying to find the global maxima of this function ...
• 231
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### Partial Derivative after Numerical Integration of a Complicated Expression with Singularity at Zero

I want to generate Fig no. 2,3,4 from https://arxiv.org/pdf/2212.08237 with the help of the following equations. In Fig 3 t_(opt) is the time Q_T reaches its max value Q_T(opt) for each T. Here is ...
1k views

### How to draw a number of circles inscribed in a square so that the sum of the radii of the circle is greatest?

I have a square with length of side is $a$. How to draw a number of circles inscribed in a square so that the sum of the radii of the circle is greatest? In the below picture is six circles inscribed ...
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1 vote
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### Why does RegionPlot handle Euler's identity differently for functions and direct expressions?

Edit When I change the x range (e.g. {x,1,3}) I get the same error also for the direct expression. Thus, the problem exists either way and I assume it just evaluated different points? Problem I want ...
187 views

### Find maximum and minimum

I have been trying to find the max and minimum values and make it to a list. I have been using some of the previous forms and it doesn´t work.This is my function: ...
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### How to find optimal solution

I want to ask something. Right now, I want to try to find the optimal solution from a function in a paper. here is the function : And here is the numerical example : There is solution procedure that ...
92 views

### General Trend of a ListLogLinearPlot

I have a data file. I must plot this using ListLogLinearPlot and identify the trend (or the mean). Below is my code for Importing the data file and plotting it. <...
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### Maximize a function of $x$ and $y$ where $x^2 +y^2 \leq 1$

I have the following function: $f(x,y) = x(y^2-x^2)- \frac{(x^2 +y^2)^2}{2\rho}+\frac{3x^2(y^2-4x^2)}{\rho}$ where $\rho>0$ is a constant. My goal is to find the maximum value of this function ...
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### How to maximize over a set containing an isolated point?

How can I maximize a function F over a set composed by a compact set like [a, b], plus a single isolated point, like $[a, b] \cup \{p\}$? I cannot code the isolated point part.
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### How to highlight top N elements in each table column?

I have tables with column and row headings, similar to this one: table = {{"",0.1,0.01}, {{1,0},1,3}, {{1,1},2,4}} I want to highlight top N elements in ...
1 vote
96 views

### An issue concerning the Maximize command in Mathematica [closed]

I have two sets. One set consists of constants and the other one consists of expressions depending on two variables "a" and "b". I find absolute values of correlations between the ...
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### How can I compute the maximum value of a ConditionalExpression?

If we use GeometricSolveValues in version 14.0, we can use this code to get a ConditionalExpression expr: ...
• 27k
1 vote
64 views

### Is a four-variable function less than one?

I have the following function of four variables f=Sqrt[(1 + w - x + 4 y z) - Sqrt[4 (-w + x) + (1 + w - x + 4 y z)^2]]/Sqrt[2] I want to show that $f(w,x,y,z)<1$...
98 views

### Find analytical expression for t as a function of x for first maximum in a periodic function

I have the following expression: 3 Csc[2 \[Pi] x t] Sin[4 \[Pi] x t]^2 I know the first maximum occurs at: ...
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1 vote
100 views

### How to calculate maximum between two or more lists element by element and also the index corresponding to the maximum element?

I am looking for a function say f such that for example f[{a1,b1,c1},{a2,b2,c2}] will give {Max[a1,a2],Max[b1,b2],Max[c1,c2]} and also a function g say such that g[{{a1, a2, a3}, {b1, b2, b3}},{{c1, ...
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1 vote
95 views

### Finding the maximum of a symbolic piecewise function

I have the function: coded as: ...
81 views

### Maximize does not finish or does not work

I need to maximize the following expression over the two variables $d$ and $a$, in terms of the parameters $t, m, k$: ...
97 views

### Minimax problem where a combination of Minimize and Maximize gives no result at all

I rarely use Mathematica, but I usually do not have any problem with simple commands like Minimize or Maximize. I have find to ...
173 views

### Is it possible to ask Mathematica to obtain the function describing the upper and lower boundaries of a combinations of functions?

Assume that I have three one-variable non-periodic functions $f(x),g(x),h(x)$ for $x>0$. The question is: is it possible to ask Mathematica to obtain the function describing the upper and lower ...
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1 vote
122 views

### ArgMax returns the input

I am new to Mathematica so I don't know if I am missing something. I am trying to use ArgMax for a specific function I have, which includes ...
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1 vote
222 views

### How can't we find the maximum value of this?

Maximize[{ω, -(π/6) + ( k π)/ω <= π, -(π/ 6) + ((k + 1) π)/ω >= (4 π)/3, ω > 0, k ∈ Integers}, {k, ω}] // FullSimplify ...
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### 3D plot not working, find max/min points [closed]

Im trying to plot this graph in mathematica: (x+y)sin(x-y) And this is my in- and output: Plot3D[(x + y) (Sin[x - y]), {x, -50, 50}, {y, -50, 50}] The output is ...
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1 vote
104 views

### Finding Max/Min of interpolated function and average value above/below the x axis

I have the below code used to create an interpolation function that will plot the difference between two interpolated functions (to compare between different periods of time). However, I would like to ...
146 views

### Is it possible to ask Mathematica to find those points $(x,y)$ at which the given function may reach its global/local extrema?

I have this two-variable function $f(x,y)$ for {x,-Pi,Pi} and {y,-Pi,Pi} in which $\{a,b,c\}$ are real parameters (can be ...
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### Is it possible to obtain the symbolic expression for the maximum value of a function?

Is it possible to obtain the symbolic expression for the maximum value of out as a function of A,...
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### NMaxValue - function is not a real number

I'm trying to use NMaxValue to numerically find maximal values of the function F[z]. The problematic part of my code is as ...
168 views

### Getting an exact value from FindMinimum [closed]

FindMinimum[{(Sin[a]^2 + Sin[b]^2)/Sin[c]^2, a + 2 b == π/2 && a + b + c == π && a > 0 && b > 0}, {a, b, c}] The numerical ...
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39 views

### Maximizing functions with statements similar but result different

I would like to know why when I maximize the sum of two functions with similar expressions (Qu and Qm), it gives me different results (nu and nm), since they should be the same results because the ...
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### Finding maximum of 2D interpolating function as a function of one of the variables

I am solving a 2D PDE in space and time b(r,t) and would like to find the maximum value of b in space as a function of time t. Using the solution for maximising a 1D interpolating function from here, ...
65 views

### extremum points

I'm trying to find Min and Max points of the polynomial below, but it seems that the expression is very complicated to mathematical, I've tried a numerical function, such as NMinimize, NRoots, Solve, ...
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225 views

### How to calculate the maximum value of $x$ which satisfy the conditions $g(x,y)=0$ and $f(x,y)>1$?

I have two functions $f(x,y)$ and $g(x,y)$ over the domains $1<x< 2$ and $0<y<\pi$. I use ContourPlot to ses those values of $(x,y)$ for which \$g(...
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156 views

### Find maximum value of a function - wrong output? [closed]

I want to find the local maximum value of the function: where the domain is 0 < x < 3/2. Wolfram|Alpha gives me the correct answer while Mathematica gives me a totally different answer. Why is ...
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1 vote