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    Hi,

    I have a quick question about the "second derivative test".

    Suppose you found out your stationary points and then test the coordinates in this thingy

    D=f_{xx}\cdot f_{yy} - (f_{xy})^{2}

    If D < 0 then the stationary point is a saddle point.

    However, if I found that \displaystyle \frac{\partial^{2}f}{\partial x^{2}} > 0 or < 0 , does this change anything or does the point remain a saddle?

    Also does \displaystyle \frac{\partial^{2}f}{\partial x^{2}} = 0 tell you anything?

    Thanks in advance.
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    (Original post by ManLike007)
    Hi,

    I have a quick question about the "second derivative test".

    Suppose you found out your stationary points and then test the coordinates in this thingy

    D=f_{xx}\cdot f_{yy} - (f_{xy})^{2}

    If D < 0 then the stationary point is a saddle point.

    However, if I found that \displaystyle \frac{\partial^{2}f}{\partial x^{2}} > 0 or < 0 , does this change anything or does the point remain a saddle?

    Also does \displaystyle \frac{\partial^{2}f}{\partial x^{2}} = 0 tell you anything?

    Thanks in advance.
    If D<0 then it's a saddle point regardless of whether f_{xx}>0 or f_{xx}<0

    f_{xx}=0 implies D \leq 0 so yes, it tells you that you have either a saddle point (if f_{xy}\neq 0) or the test is inconclusive (if f_{xy} = 0). Alternatively, we can just say that f_{xx} = 0 implies no relative max/min
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    (Original post by RDKGames)
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    Ah ok I see, thank you very much sir
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    (Original post by RDKGames)
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    Really sorry to bump this thread but I require your assistance again if you don't mind!

    Suppose you had two local minimum points for example, how would I determine which point is global or local?

    (Just to clarify, I know both points are technically local minimum points but I want to know which one is global or not)
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    (Original post by ManLike007)
    Really sorry to bump this thread but I require your assistance again if you don't mind!

    Suppose you had two local minimum points for example, how would I determine which point is global or local?

    (Just to clarify, I know both points are technically local minimum points but I want to know which one is global or not)
    One has greater f value than the other. If the point is global max/min, then f takes lower/greater values for all other x,y
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    (Original post by RDKGames)
    One has greater f value than the other. If the point is global max/min, then f takes lower/greater values for all other x,y
    Ohhh ok, much appreciated for all your time and help
 
 
 
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