### 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)**and

*dy/dx=0***(2)**

*dy/dx is possitive at c-h ;*

**dy/dx is negative at c+h****--- Criterion B :- (1)**and

*dy/dx=0***(2)**

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

**For a minimum at x=d :-****--- Criterion A :- (1)**

*and*

**dy/dx=0****(2)**

*is negative at*

**dy/dx**

**d-h ;**

**dy/dx is positive at d+h****--- Criterion B :- (1)**

*and*

**dy/dx=0****(2)**

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