# 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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Akinchay Vikas Jain on 13 Dec 2021
Commented: HARA TEJ DIVI on 14 Feb 2022
Find the maxima and minima of two variable function f(x,y)=x^4+y^4-4xy+1
##### 2 CommentsShowHide 1 older comment
John D'Errico on 15 Dec 2021

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 CommentsShowHide 1 older comment
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.
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HARA TEJ DIVI on 14 Feb 2022
How to do it by using for loop