Local Extrema
The Hessian Matrix is defined as
For the twice continuously differentiable function with grad f(x0,y0) = 0 and symetric matrix :
i) det Hess > 0 and a1,1 > 0 then f has a local minimum at (x0,y0)
ii) det Hess > 0 and a1,1 < 0 then f has a local maximum at (x0,y0)
iii) det Hess < 0 then f has a saddle point at (x0,y0)
Click Init button to start
You can move the point on the surface to find a maximum, minimum or saddle point.
Check "auto" if you want the point to move automatically to one local maximum point.
Check "curves" to draw curves along gradient and normal to it, and level curve for current point.
You can enter other functions like:
f(x,y) = x*y , f(x,y) = 0.5(x³ + x² - x) - 0.5y² , etc.
(Original idea from Andreas Lindner https://ggbm.at/rVmxKNSE)