Let f:(0,\pi)\to\mathbb{R} be a twice differentiable function such that \text{lim}_{t\to\infty}\frac{f(x)sint-f(t)sinx}{t-x}=\sin^2x for all x∊(0,\pi).If f(\pi/6)=-\pi/12,then which of the following statement (s) is (are) TRUE? [JEE Adv 2018 P2]

f(x) < x^4/6-x^2 for all x∊(0,\pi)

There exists \alpha∊(0,\pi) such that f'(\alpha)=0

Limits, Continuity and Differentiability

Section: Mathematics

Question : 23 of 51

Marks: +1, -0

Let f:(0,π)→ℝ be a twice differentiable function such that

lim

t→∞

f(x)sint−f(t)sinx

t−x

=sin2x for all x∊(0,π).If f(

)=−

,then which of the following statement (s) is (are) TRUE?

[JEE Adv 2018 P2]

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