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, [11-Apr-2023 shift 1]

Question

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,  [11-Apr-2023 shift 1]

Examsnet · Accepted Answer

Correct Answer is : Both the statements (A) and (B) are true

JEE Mains 11-Apr-2023 Shift 1 Solved Paper