Question

find all locations and values of local maxima and minima and the location of the saddle points for:
\[f(x,y) = x ^{3}+y ^{3}+3x ^{2}-3y ^{2}-9\]

Answer 1

\[f(x,y) = x ^{3}+y ^{3}+3x ^{2}-3y ^{2}-9\]

Answer 2

equate first order derivatives and solve for critical points. the calculate the hessian and see if it's positive or negative.
http://www.math.oregonstate.edu/home/programs/undergrad/CalculusQuestStudyGuides/vcalc/min_max/min_max.html

Answer 3

*then

Answer 4

thank you very much! I ended up following those steps very well to my success!