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  • Critical points: هى النقاط التى تكون عندها مشتقة الدالة تساوى صفر او غير موجودة .
  • A function of two variables has a local maximum at
    (a, b) if f (x, y) =< f (a, b) when (x, y) is near (a, b)
  • A function of two variables has a local minimum at
    (a, b) if f (x, y) >= f (a, b) when (x, y) is near (a, b)
  • Second Derivatives Test:

 

  • To find the absolute maximum and minimum values of a continuous function f on a closed, bounded set D:
  1. Find the values of F at the critical points of F in D.
  2. Find the extreme values of  F on the boundary of D.
  3. The largest of the values from steps 1 and 2 is the absolute maximum value; the smallest of these values is the absolute minimum value

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