Paragraph:
Read the following passage and answer the questions.
For every function \(f(x)\) which is twice differentiable, these will be good approximation of \(\int_a^b f(x) d x \cong\left(\frac{b-a}{2}\right)\{f(a)+f(b)\}\). Now, if we take \(c=\frac{a+b}{2}\), then using above again, we get \(\int_a^b f(x) d x=\int_a^c f(x) d x+\int_c^b f(x) d x \cong \frac{b-a}{4}\{f(a)+f(b)+2 f(c)\}\) and so on.
We get approximation for value of \(\int_a^b f(x) d x\).Question:
If \(f^{\prime \prime}(x) < 0, \forall x \in(a, b), c(c, f(c))\) is point of maxima where \(c \in(a, b)\), then \(f^{\prime}(c)\) is

1. A
   \(\frac{f(b)-f(a)}{b-a}\)
   
2. B
   \(3\left(\frac{f(b)-f(a)}{b-a}\right)\)
   
3. C
   \(2\left(\frac{f(b)-f(a)}{b-a}\right)\)
   
4. D
   0