Let f : (0, π) → R be a twice differentiable function such that _ t x f(x) t-f(t) x t-x =…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let f : (0, π) → R be a twice differentiable function such that \(\lim _{t \rightarrow x} \frac{f(x) \sin t-f(t) \sin x}{t-x}=\sin ^{2} x\) for all x ∈ (0, π).
If \(f\left(\frac{\pi}{6}\right)=-\frac{\pi}{12}\), then which of the following statement(s) is (are) TRUE?
If \(f\left(\frac{\pi}{6}\right)=-\frac{\pi}{12}\), then which of the following statement(s) is (are) TRUE?
- f(x) <
– x2 for all x ∈(0, p) - There exists a ∈ (0, p) such that f ′(a) = 0
Answer
(C) There exists a ∈ (0, p ) such that f ′ ( a ) = 0
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