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 [2,4] (B): f(x) ≥ 1/8, for all x [2,4] Then,

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

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

Limit, Continuity and Differentiability: JEE Main 2023 Mathematics question

JEE Main 2023 · 11 Apr, Morning shift · Q2702

JEE Main 202311 Apr, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let

f:[2,4] \rightarrow \mathbb{R}

be a differentiable function such that

\left(x \log _{e} x\right) f^{\prime}(x)+\left(\log _{e} x\right) 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,

JEE Main 2023 · 11 Apr, Morning shift · Q2702

JEE Main 202311 Apr, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let

f:[2,4] \rightarrow \mathbb{R}

be a differentiable function such that

\left(x \log _{e} x\right) f^{\prime}(x)+\left(\log _{e} x\right) 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,