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Let the definite integral be defined by the formula `int_(a)^(b)f(x)dx=(b-a)/2(f(a)+f(b))`. For more accurate result, for `c epsilon (a,b), ` we can use `int_(a)^(b)f(x)dx=int_(a)^(c)f(x)dx+int_(c)^(b)f(x)dx=F(c)` so that for `c=(a+b)/2` we get `int_(a)^(b)f(x)dx=(b-a)/4(f(a)+f(b)+2f(c))`.
If `f''(x)lt0 AA x epsilon (a,b)` and `c` is `a` point such that `altcltb`, and `(c,f(c))` is the point lying on the curve for which `F(c)` is maximum then `f'(c)` is equal to

A

`(f(b)-f(a))/(b-a)`

B

`3[(f(b)-f(a))/(b-a)]`

C

`2[(f(b)-f(a))/(b-a)]`

D

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The correct Answer is:
A
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