Local Extrema

Below, we have a function which three parameters a, b, c. Slide the values for a, b, and c around to see how it changes the shape of the graph. Note that, if [math]f\left(x,y\right)=ax^2+bxy+cy^2[/math], then[br][math]f_{xx}=2a[/math], [math]f_{yy}=2c[/math], [math]f_{xy}=b[/math], and [math]D=f_{xx}f_{yy}-\left(f_{xy}\right)^2=4ac-b^2[/math].

Information: Local Extrema