# Write a MATLAB code to Find the maxima and minima of two variable function f(x,y)=x^4+y^4-4xy+1

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Find the maxima and minima of two variable function f(x,y)=x^4+y^4-4xy+1

##### 2 Comments

Yusuf Suer Erdem
on 13 Dec 2021

Edit your question like this please;

How to write the MATLAB code to find the maximum and minimum output of a function with 2 variables;

f(x,y)=x^4+y^4-4*x*y+1

John D'Errico
on 15 Dec 2021

### Answers (2)

Yusuf Suer Erdem
on 13 Dec 2021

Hi Akinchay, try these codes below please;

clc;

clear;

close all;

xMin = -2;

xMax = 2;

yMin = -2;

yMax = 2;

numPoints = 200;

xv = linspace(xMin, xMax, numPoints);

yv = linspace(yMin, yMax, numPoints);

[x, y] = meshgrid(xv, yv);

% f(x,y) = x.^4 + y.^4 - 4.*x.*y + 1

fprintf('Creating function.\n');

f = x.^4 + y.^4 - 4.*x.*y + 1;

fprintf('Creating surface plot.\n');

surf(x, y, f, 'LineStyle', 'none');

xlabel('x', 'FontSize', 20);

ylabel('y', 'FontSize', 20);

zlabel('f', 'FontSize', 20);

title('f(x,y) = x.^4 + y.^4 - 4.*x.*y + 1', 'FontSize', 20);

colorbar;

maxValue = max(abs(f(:)));

minValue = min(abs(f(:)));

fprintf('The max of f = %f.\nThe min of f = %f.\n', maxValue, minValue);

##### 2 Comments

Torsten
on 13 Dec 2021

Not in your case because some solutions of p=0 and q=0 will be complex-valued.

Torsten
on 13 Dec 2021

Edited: Torsten
on 13 Dec 2021

syms x y f(x,y)

f(x,y)=x^4+y^4-4*x*y+1;

dfx=diff(f,x);

dfy=diff(f,y);

eqns=[dfx==0,dfy==0];

vars=[x y];

S=solve(eqns,vars,'Real',true)

@Yusuf Suer Erdem: I think local minima and maxima are meant in the exercise.

##### 2 Comments

Yusuf Suer Erdem
on 14 Dec 2021

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