Hi Tommaso,
The issue you're encountering is because you're trying to plot the function along the line "y = 5 - t", which doesn't seem to be related to your constraint.
The constraint “g(x,y) == 0” is a hyperbola in the x-y plane. To plot the function “f(x,y) = x*y” restricted to this constraint, you need to express “y” in terms of “x” from the constraint equation, and then substitute this into the function “f(x,y)”.
You can solve the constraint equation “g(x,y) == 0” for “y” to get two possible solutions (branches of the hyperbola). Then, create two new functions “y1(t)” and “y2(t)” for each branch of the hyperbola by substituting “x” with “t” in the solutions. Finally, use these functions in “fplot3” to plot the function “f(x,y) = x*y” along these lines.
Here's the updated part of your code:
g(x,y) = x^2 +y^2 -4*x*y -1;
sol = solve(g == 0, y); % solve constraint for y
y1(t) = subs(sol(1), x, t); % create function for first branch
y2(t) = subs(sol(2), x, t); % create function for second branch
fplot3(t, y1(t), f(t,y1(t)),'r--', [0 5], 'LineWidth', 2) % plot first branch
fplot3(t, y2(t), f(t,y2(t)),'r--', [0 5], 'LineWidth', 2) % plot second branch
Now the dotted lines should co-incide, as expected.
Hope this helps.
