### 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 .

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 .