Teaching JKPSC Lecturership Mock Test Series 2024-25 Mathematical Science Analysis Continuity & Differentiability
Let u: R → R be a twice continuously differentiable function such that u(0) > 0 and u′ (0) > 0. Suppose u satisfies \(u^{\prime \prime}(x)=\frac{u(x)}{1+x^{2}}\) for all x ∈ R.
Consider the following two statements:
I. The function uu′ is monotonically increasing on [0, ∞).
II. The function u is monotonically increasing on [0, ∞).
Then which one of the following is correct?
1
Both I and II are false.
2
Both I and II are true.
3
I is false, but II is true.
4
I is true, but II is false.