Second partial derivative test example, part 2

Continuing the worked example from the previous video, now classifying each critical point.

[tejindersingh]

at 5:30 i think there is a mistake because for the (sqrt3, 1) you put only sqrt3 for fxy which is 6x but it should be (6(sqrt3))^2 so (sqrt3, 1) : (0)(-12)- (6(sqrt3))^2 instead of
(0)(-12)-(sqrt3)

[alejrandom]

4:34
Grant: "what is 18 times 6?"
Me: 6*10+6*8...
Grant: "36 times 3"

[wassimzaki]

How about the absolute max and min? How can we know if the local max in this case (at x=0 and y=0) is an absolute max or not?

[ryanmike]

H = det(Hessian_f). Any relevance? We're dealing with functions of two variables, does this second partial derivative test generalize for f(x_1, x_2, ...)?

[ryanmike]

Also, what about stationary points where chopping with constant x or y yields not a local max/min, but an inflection point. Ex: (0, 0) on f(x, y)=y^3-x^2 or f(x, y)=y^3-x^3. Still saddle points?

[pratik]

How can we make sure that its global maxima/minima not the local maxima/minima??

[polharbor]

at 6:18
Shouldn't - ( - sqrt3)^2 equal positive 3 ??

[BenlshTracker]

the way this guys speaks is so similar to sal that it is a lil scary :O

[Thadnill]

what if H turns out positive, but fxx = positive and fyy = negative (or vice versa), is it a maximum or a minimum then?

[twistedlot]

cool! just a tiny hair away from mentioning the Hessian

[alvin]

can anyone help me find the critical point of f(x, y) = e^x cosy