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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 . **