Let f : [ 2 , 4 ] R be a differentiable function such that ( x log e x ) f ' ( x ) + ( log e x ) f ( x ) + f ( x ) 1 , x [ 2 , 4 ] with f ( 2 ) = 1 2 and f ( 4 ) = 1 4 . Consider the following two statements: (A) : f ( x ) 1 , for all x [ 2 ,

STUDY MATERIALS
COURSES
MORE
SUCCESS STORY
ADMISSION
STORE

Back

JEE ADVANCE

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

JEE MAIN

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

NEET

CLASS XI - XII
CRASH COURSE

CLASS XI - XII

CRASH COURSE

BITSAT

CLASS XI - XII

CLASS XI - XII

CBSE BOARD

CLASS IX

CLASS X

CLASS XI

CLASS XII

CLASS VI

CLASS VII

CLASS VIII

UP BOARD

CLASS IX
CLASS X
CLASS XI
CLASS XII

CLASS IX

CLASS X

CLASS XI

CLASS XII

CUET

CRASH COURSE

CRASH COURSE

Courses

CLASSROOM COURSES
ONLINE COURSES

ONLINE COURSES

More

Solution

Q.
Let $f : [2, 4] \to R$ be a differentiable function such that $(x \log_{e} x) f' (x) + (\log_{e} x) f (x) + f (x) \geq 1, x \in [2, 4]$ with $f (2) = \frac{1}{2}$ and $f (4) = \frac{1}{4}$ .

Consider the following two statements:

(A) : $f (x) \leq 1$ , for all $x \in [2, 4]$

(B) : $f (x) \geq \frac{1}{8}$ , for all $x \in [2, 4]$

Then,

1 Only statement (B) is true

2 Neither statement (A) nor statement (B) is true

3 Both the statements (A) and (B) are true

4 Only statement (A) is true

Ans.
(3)

Want Us to Email you About Special Offers & Updates?