Posted by tony on .
Using the Second Partials Test
Find the relative extrema of f(x,y)=x^(3)+4xy2y^(2)+1

cal 
Damon,
fx = 3 x^2 + 4 y
level if x = +/(4y/3)^.5
fxx = 6 x
fxy = 4
fy = 4 x  4 y level when x = y
fyy = 4
fyx = 4
extreme only when x = y = 0
H matrix
6 x 4
4 4
det = 6x  4
if x = 0, det = 4
if det <0 then (0,0) is a "saddle point"