(a,d)

f '(x) =

Let g(x) = sin x – x cos x

g'(x) = cos x + x sin x – cos x

g'(x) > 0 ∀ x ∈ (0, π /2)

g(x)

g(0) < g(x)

0 < sin x – x cos x

∴ f '(x) > 0

f(x) Let α = π /12, β = π /4, r = 5 π /12

⇒ f( α ) < f( β ) < f(r)

Let H(x) = 2 (x –f( β )) (x – f(r)) + 3 (x – f( α )) (x – f(r)) + 4 (x – f( α )) (x – f( β ))

H (f(r)) > 0, H(f( β )) < 0, H(f(r)) > 0

⇒ one root in (f(r), f( β )) (f(r), f( β ))

and other in (f( β ), f(r)) (f( β ), f(r))

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