The area (in sq. units) of the largest rectangle A B C D whose vertices A and B lie on the x -axis and vertices C and D lie on the parabola, y = x 2 - 1 below the x -axis, is :

Step-by-step solution

A ( α , 0 ) , β ( - α , 0 ) ⇒ D α , α 2 - 1 A r e a   ( A B C D )   =   ( A B )   ( A D ) ⇒ S = ( 2 α ) 1 - α 2 = 2 α - 2 α 3 d s d α = 2 - 6 α 2 = 0 ⇒ α 2 = 1 3 ⇒ α = 1 3  Area  = 2 α - 2 α 3 = 2 3 - 2 3 3 = 4 3 3