Stationary Points in Multivariable Functions
# Local Extrema, Critical Points, & Saddle Points of Multivariable Functions #
Multivariable function: z=f(x,y)
graph TD A[Start] -->|fₓ=0 & f_y=0| B("Stationary points (x₀,y₀)") B --> C[D=rt-s^2=f_xxf_yy-f_xy^2] C -->D[D>0] C -->E[D<0] E -->F[Saddle Point] D -->G["f_xx>0"] D -->H["f_xx<0"] G ---|like upward parabola| I["Local Min"] H ---|like downward parabola| J["Local Max"]