Consider the function f ( )=4 ( ^2 + ^4 ) What is the minimum value of the function f( ) ?

Step-by-step solution

aligned f( )= & 4 ( ^2 + ^4 ) = & 4 ( ^2 + ^2 (1- ^2 ) ) = & 4 ( ^2 + ^2 - ^2 ^2 ) = & 4 (1- 1 4 ^2 2 ) & [ 2 =2 ] aligned For minimum value of f( ), ^2 2 should be maximum i.e. ^2 2 =1 . .f( ) |_ =4 (1- 1 4 (1) )=4 3 4 =3