Consider the region R= (x, y): x y 9- 11 3 x^2, x 0 . The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R , is:

Step-by-step solution

t . (9- 11 t ^2 3 - t ) aligned & A =9 t - t ^2- 11 3 t ^3 & dA dt =9-2 t -11 t ^2 & 11 t ^2+2 t -9=0 & 11 t ^2+11 t -9 t -9=0 & t =-1 & t = 9 11 aligned aligned & largest area = 9 11 (9- 11 3 , 81 121 - 9 11 ) & = 9 11 63 11 = 567 121 aligned