wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

The absolute difference between the greatest and the least values of the function f(x)=x(lnx2) on [1,e2] is

A
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
e
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
e2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B e
f(x)=x(lnx2)
f(x)=x(1x)+(lnx2)=lnx1
f(x)=lnx1
f(x)=0x=e
For x[1,e), f(x)<0 and for x(e,e2], f(x)>0
So, the minimum value of f(x) occurs at x=e

Now, f(1)=2
f(e)=e (least)
f(e2)=0 (greatest)

Hence, |f(e2)f(e)|=|0(e)|=e

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon