Posted by **tony** on Sunday, March 16, 2014 at 1:08pm.

Using the Second Partials Test

Find the relative extrema of f(x,y)=-x^(3)+4xy-2y^(2)+1

- cal -
**Damon**, Sunday, March 16, 2014 at 1:35pm
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"

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