If f(x) is a polynomial function satisfying the condition f(tanx).f(cotx)=f(tanx)+f(cotx) and f(2) = 9 then find the value of
$\frac{f ^{'} ( 2 )}{6}$

Question

If f(x) is a polynomial function satisfying the condition f(tanx).f(cotx)=f(tanx)+f(cotx) and f(2) = 9 then find the value of 6 f ′ ( 2 ) ​

TestHub · Accepted Answer

Putting tan x = t , we get f ( t ) is a polynomial function of the form, f ( t ) = ± t n + 1 when t = 2, ​ f ( 2 ) = 9 ⇒ n = 3 ∴ f ( t ) = t 3 + 1 f ′ ( 2 ) = 12 ∴ 6 f ′ ( 2 ) ​ = 2 ​

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