JEE MATHEMATICS MCQ: DIFFERENTIATION

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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}{2}

.

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,

View answer and explanation

Correct option: C

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

Option D (

\frac{{5}}{{2}}

) is correct because after finding the possible values of α using the given conditions, the sum of these values is equal to 5/2.

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