Question

The following code must be written using matlab

Create a contour plot of the following function f(x,y) = (x+y^2-10)^2 +(x^2+y^2+8) in range [-6,6] for both x and y

Clearly indicate in the plot the coordinates of the minimum ponts and the the corresponding function values in these points

Answer 1

ANSWER:

• I have provided the properly commented code in both text and image format so you can easily copy the code as well as check for correct indentation.
• I have provided the output image of the code so you can easily cross-check for the correct output of the code.
• Have a nice and healthy day!!

CODE TEXT

% contour plot

% defining function f

f = @(x,y) (x + y.^2 - 10).^2 + (x.^2 + y.^2 + 8);

% defining x , y vector from -6 to 6

x = -6:0.2:6;

y = -6:0.2:6;

% generating meshgrid using x and y vector

[X,Y] = meshgrid(x,y);

Z = f(X,Y);

% ploting contour using contour function of matlab,

contour(X,Y,Z);

% labeling plot

xlabel("x value");

ylabel("y value");

title("Contour on function in xy range [-6,6]");

% holding plot to display min values

hold on;

% finding min value in Z, using min function

minZ = min(Z(:));

% finding locations for minZ in Z

[xMin,yMin] = find(Z==minZ);

% ploting points for minZ using plot3 function of matlab

plot3(X(xMin,yMin),Y(xMin,yMin),Z(xMin,yMin),"ro");

% displaying legend

legend("Z contour","Min Points");

CODE IMAGE

OUTPUT IMAGE