MATLAB for approximate values of EXTREMA SADDLE POINTS Function of two variables
For the classes of atul roy
MATLAB CODE
syms x y
f=x^3-8*x^2*y-24*x*y+6*x*y^2+y^4
fsurf(f,[-100 300 -10 50])
hold off
fx=diff(f,x)
fy=diff(f,y)
fimplicit(fx==0,[-100 300 -10 50])
hold on
fimplicit(fy==0,[-100 300 -10 50])
hold off
fimplicit(fx==0,[-10 10 -10 10])
hold on
fimplicit(fy==0,[-10 10 -10 10])
hold off
g(x,y)=x^3-8*x^2*y-24*x*y+6*x*y^2+y^4
g(180,35)
g(-5,-2)
fcontour(f,"LevelList",-1000000:10000:1000)
axis([-100 300 -10 50])
hold off
fcontour(f,"LevelList",-150:10:50)
axis([-10 10 -10 10])
hold off
fsurf(f,[-100 300 -10 50],'MeshDensity',60)
axis([-100 300 -10 50 -1000000 10])
hold off
fsurf(f,[-10 1 -10 1],'MeshDensity',60)
axis([-10 1 -10 1 -200 10])
hold off
z=@(x,y) [3*x^2-16*x*y+6*y^2-24*y,-8*x^2+12*x*y-24*x+4*y^3]
fsolve(@(u) z(u(1),u(2)),[-4,-3])
fsolve(@(u) z(u(1),u(2)),[-4.7,-1.6])
fsolve(@(u) z(u(1),u(2)),[177,36])
hold off
double(g(-3.3206,-3.0434))
double(g(-5.0064,-1.6214))
double(g(176.4245,35.4493))