; x = - - When x = – , f ll (– ) = (– ) + = – < ` f ( x ) attains local maximum at x = – and local maximum value is obtained from ( ) by substituting the value x = – . f (– ) = (– ) + (– ) – (– ) = – + + = . When x = , f ll ( ) = ( ) + = f ( x ) attains local minimum at x = and the local minimum value is obtained by substituting x = in ( ). f ( ) = ( ) + ( ) – ( ) = – Extremum values are – and .
Example . Find the absolute (global) maximum and absolute minimum of the function f ( x )= x – x + x + in the interval [– , ] Solution : f ( x ) = x - x + x + … ( ) f l ( x ) = x – x + = ( x – x + ) f l ( x ) = Þ ( x – x + )= Þ ( x – )( x – )= Þ x = ± (or) x = ± Of these four points – ± ∈− , and ∉− From ( ) f (– ) = = – When x = f ( ) = = When x = – f (– ) = =– Absolute maximum is and Absolute minimum is - .