[問題] 2階微分求極值的問題--有關regression

[rpm (我永遠的旭仔..)]

老師出了一題統計公課
因為實在遠離數學太久了~~
可以請高手幫我解答或提示我那本參考書可以找到答案嗎? 感激不盡 T T

題目是:
simple regression
sample:(x1,y1),(x2,y2),...(xn,yn)

      Y=a+bx+ε

           ^   ^
      E(Y)=a + b x

               2
      E~ N(0,σ )

         n     2   n                2
      L= Σ εi  = Σ  [yi-(a+b*xi)]
         i=1       i=1
                             ^          _ _       2   _2
δL/δa=0 ,  δL/δb=0  證明:b =Σxiyi-nx y / Σxi - nx

                             ^   _  ^   _
                             a = y- b * x

接下來還要證明下面四項,D式子我不太會微分 >"<


Let L be a function of two variables with continuous second-order partial
derivatives in some circle centered at a critical point(a,b)
                                      2
and let  D=Lxx(a,b)Lyy(a,b)-{Lxy(a,b)}

(I)   if D > 0 , Lxx(a,b)>0 ,then L has a relative minimum at (a,b)
(II)  if D > 0 , Lxx(a,b)<0 ,then L has a relative maximum at (a,b)
(III) if D < 0 , then L has a saddle point at (a,b)
(IV)  if D = 0 , then no conclusion can be drown



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