question_answer

The sum of infinite terms of a decreasing G.P. is equal to the greatest value of the function \[f(x)={{x}^{3}}+3x-9\] in the interval \[\left[ -\,2,3 \right]\] and the difference between the first two terms is f'(0). Then, the common ratio of a G.P. is

A)  \[\frac{2}{3}\] 

B)  \[\frac{1}{3}\]

C)  \[\frac{-\,5}{3}\]                                  

D)  \[\frac{-\,4}{3}\]

E)  None of these