A rectangle has one side on the positive y-axis and one side on the x-axis. The upper right hand vertex of the rectangle lies on the curve y=ℓnxx2 The maximum area of the rectangle is
A
e−1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
e−1/2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
e1/2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is Ae−1 Vertices of rectangle are (0,0),(x,0),(0,y),(x,y) Therefore, Area A=xy=lnxx For maximum area dAdx=1−lnxx2=0 ⇒x=e now, d2Adx2=−(3−2lnx)x3 at x=e, d2Adx2<0 Therefore, A is maximum at x=e Thus, A=1/e Ans: A