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

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

[Yusuf Suer Erdem]

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]

Please stop posting your homework assignment questions. Answers is not a service where we do your homework.

Answer 1

[Yusuf Suer Erdem]

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);

[Akinchay Vikas Jain]

Is this the right code for it ?

[Torsten]

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

Answer 2

[Torsten]

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.

[Yusuf Suer Erdem]

@Torsten Hi Torsten, if it is asked local maxima and local minima, you are right. Determining the points where diff(f)==0 will give us local minima and maxima.

[HARA TEJ DIVI]

How to do it by using for loop