#2 var function description
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radiant vortex
Recall how to tell the type of critical point from the hessian matrix.
ocean tusk
Recall how to tell the type of critical point from the hessian matrix.
I never learned that but
D=(fxx)(fyy)-(fxy)^2=16=local max?
radiant vortex
I never learned that but
D=(fxx)(fyy)-(fxy)^2=16=local max?
No, that's not enough to say that.
Let me describe the general approach for a function of two variables.
ocean tusk
I never learned that but
D=(fxx)(fyy)-(fxy)^2=16=local max?
And because fxx(1,1)<0? This is teachers notes
radiant vortex
Suppose:
A = ∂^2 f/∂x^2
B = ∂^2 f/(∂x∂y)
C = ∂^2 f/∂y^2
All derivatives are evaluated at a point r0.
Then we have D = det(H) = AC - B^2. Then there are four cases.
- If D > 0 and A > 0, then r0 is a minimum point.
- If D > 0 and A < 0, then r0 is a maximum point.
- If D < 0, then r0 is a saddle point.
- If D = 0, then this test is inconclusive.
So, what can you say about the given point?
ocean tusk
Local max?
radiant vortex
Local max?
Yes, nice!
ocean tusk
Alright thanks for the explanation!