f(x,y)=f(x0,y0)+△x f_x'(x0,y0)+△y f_y'(x0,y0)+1/2[(△x)²f_xx'' (ξ,η)+2△x △y f_xy''(ξ,η)+(△y)² f_yy''(ξ,η)]
=f(x0,y0)+1/2[(△x)²f_xx'' (ξ,η)+2△x △y f_xy''(ξ,η)+(△y)² f_yy''(ξ,η)]
→f(x0,y0)+1/2[A(△x)²+2B△x △y +C(△y)² ]
B²-AC<0时,中括号内符号恒定不变。A<0时,中括号内恒为负数,此时为极大值点。也就是说,在(x0,y0)邻域内,任意变动△x,△y,都会导致函数值变小,因此(x0,y0)是极大值点。A>0时,中括号内恒为正数,此时为极小值点。B²-AC>0时,中括号内符号不确定,因此不是极值点。B²-AC=0时,中括号内大于等于0,可能是极值点,也可能不是极值点。
追问谢谢啦^_^
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/caef76094b36acaf1fda9d8d7bd98d1001e99c8c?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
问一下这个到下一步为什么没有了
哦,懂了
![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/3812b31bb051f8193877703bddb44aed2e73e775?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
划线的这个具体怎么考察呀?
追答V0是什么?
追问![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/09fa513d269759eedfe81fbab5fb43166d22df03?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
这两张合起来是完整的证明,然后我也是搞不懂v0是什么
追答V0就是抛物线顶点横坐标值。当V等于V0时,u等于0,函数值不变。此时前面的近似失效,需要考虑更高阶的偏导数。