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+2 votes
12.9k views
in Mathematics by (52.9k points)

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

lim t→x (f(x) sint-f(t)sinx)/t-x= sin2x for all x∈(0,π)

If f(π/6)=-π/12, then which of the following statement(s) is (are) TRUE ?

(A) f(π/4)=π/4√2

(B) f(x)<x4/6-x2 for all x∈(0,π)

(C) There exists α∈(0,π) such that f '(α) = 0

(D) f ''(π/2)+f(π/2)=0

1 Answer

+3 votes
by (266k points)
selected by
 
Best answer

Answer: B,C,D

Solution:

Using L Hospitals rule​

f(x) = –x sin x

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