Using the Hessian Matrix to Determine the Nature of a Turning Point

Suppose I have the equation y=x^2. How would I use the Hessian Matrix in an if-else clause to determine the nature of the turning point of y=x^2? Thanks

[Torsten]

Which turning point ? y=x^2 has one extremum, but no turning points.

Answer 1

[Torsten]

If you mean the kind of extremum:

syms x
y = x^2;
dy = diff(y,x);
ddy = diff(dy,x);
sol = solve(dy==0);
ddy_at_critical_point = double(subs(ddy,sol));
maxima = sol(ddy_at_critical_point<0)

 
maxima =
 
[ empty sym ]
 

minima = sol(ddy_at_critical_point>0)

minima = 

0

unknown = sol(ddy_at_critical_point==0)

 
unknown =
 
[ empty sym ]