9f'(3) - f'(1) + 32 = 0
∫₁³ f(x)dx = 14
∫₁³ f(x)dx = 12
9f'(3) + f'(1) = 0
∫₁³ f(x)dx = ∫₁³ xf(x)dx = (f(x).x)|₁³ - ∫₁³ x²f'(x)dx = 9f(3) - f(1) - 12 = 14
f'(3) = f(3) + 3f'(3)
f'(1) = f'(1)
For option C, substitute equation 1) and 2)
9f'(3) - f'(1) + 32 ⇒ 9f(3) + 27f'(3) - f'(1) + 32
27f'(3) - f'(1) = 0
On substituting the values of f(x) we get the value as zero