来自《耶鲁大学开放课程：博弈论 第6集 第6集》

• 
  
  we're being nerdy, let's actually be a little bit careful.
  但我们还是严谨一点好啊
• 
  
  This was a first order condition or a first order necessary condition.
  这个只是一阶条件 是必要条件
• 
  
  I actually need to check the second order condition.
  实际上我们还需要验证二阶条件
• 
  
  So how do I check the second order condition?
  怎样验证二阶条件呢
• 
  
  I differentiate again, right?
  需要再次求导 是吧
• 
  
  I differentiate a second time and check the sign,
  我们对它进行二次求导然后看符号
• 
  
  so the second order condition,
  这个式子的二阶导数
• 
  
  I differentiate this expression again with respect to q1.
  就是一阶导数再对q1进行求导
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  The only place q1 appears here is here,
  只有这一处有q1
• 
  
  so when I differentiate again I'm going to get -2b
  因此二阶导数是-2b
• 
  
  and sure enough that's negative,
  它肯定是个负数了
• 
  
  which is what I wanted to know,
  这正是我们想得到的结果