Criteria of Maximum and Minimum

 


We have these two criteria for judging whether a function has a maximum or minimum at a particular point .

For a maximum at   x=c  :- 

---  Criterion A :-  (1) dy/dx=0 and
               
       (2) dy/dx  is possitive at  c-h  ;

           dy/dx  is negative at   c+h

---  Criterion B :-  (1) dy/dx=0  and

        (2)  (d/dx)(dy/dx)  is negative 

For  a minimum at   x=d  :-

---  Criterion A :-  (1)  dy/dx=0  and

      (2)  dy/dx  is negative at  d-h  ;

           dy/dx  is positive at  d+h  

---  Criterion B :-  (1)  dy/dx=0  and

     (2)  (d/dx)(dy/dx)  is positive .