Definition 6.1

Definition . Local Maximum and local Minimum A function f has a local maximum (or relative maximum) at c if there is an open interval ( a , b ) containing c such that f ( c ) ≥ f ( x ) for every x ! ( a , b ). Similarly, f has a local minimum at c if there is an open interval ( a , b ) containing c such that f ( c ) ≤ f ( x ) for every x !