What is the maximum value of 3( x- x)+4 ( ^3 x . .- ^3 x ) ?

Step-by-step solution

aligned & Let f(x)=3( x- x)+4 ( ^3 x- ^3 x ) & f^ (x)=3( x+ x)-12 x x( x+ x) & =3( x+ x)(1-2 2 x)=0 & array l x= 3 4 , 6 f^ (x)=3(- x+ x)(1-2 2 x) -3( x+ x)(-4 2 x) f^ ( 3 4 ) 0 and f^ ( 6 ) 0 array & f(x) is maximum at x= 3 4 & f ( 3 4 )=3 ( 1 2 + 1 2 )+4 ( -1 2 2 - 1 2 2 ) & =3 2 -2 2 = 2 aligned