Let f(x) be a polynomial function satisfying \[f(x).f\left( \frac{1}{x} \right)=f(x)+f\left( \frac{1}{x} \right).\] if \[f(4)=65\] and \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]are in \[GP,\] then \[f'({{l}_{1}}),f'({{l}_{2}}),f'({{l}_{3}})\] are in

Let f(x) be a polynomial function satisfying \[f(x).f\left( \frac{1}{x

1.	Let f(x) be a polynomial function satisfying \[f(x).f\left( \frac{1}{x} \right)=f(x)+f\left( \frac{1}{x} \right).\] if \[f(4)=65\] and \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]are in \[GP,\] then \[f'({{l}_{1}}),f'({{l}_{2}}),f'({{l}_{3}})\] are in
A.	AP
B.	GP
C.	HP
D.	None of these
Answer» C. HP

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Let f(x) be a polynomial function satisfying \[f(x).f\left( \frac{1}{x} \right)=f(x)+f\left( \frac{1}{x} \right).\] if \[f(4)=65\] and \[{{l}_{1}},{{l}_{2}},{{l}_{3}}\]are in \[GP,\] then \[f'({{l}_{1}}),f'({{l}_{2}}),f'({{l}_{3}})\] are in

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