Let f be a polynomial function such that f 3 x = f ′ x .   f ′ ′ x , for all x ∈ R . Then :

Question

Let f be a polynomial function such that f 3 x = f &#8242; x . &#160; f &#8242; &#8242; x , for all x &#8712; R . Then :

Aicharya · Accepted Answer

Degree of f x will be 3 f ( x ) = a x 3 + b x 2 + c x + d f 3 x = 27 a x 3 + 9 b x 2 + 3 c x + d f ' ( x ) = 3 a x 2 + 2 b x + c f &#8242; &#8242; x = 6 a x + 2 b f 3 x = f &#8242; x &#160; f &#8242; &#8242; x Comparing the coefficient, we get 27 a = 18 a 2 &#8658; a = 3 2 Also b = 0 , &#160; c = 0 , &#160; d = 0 f x = 3 2 x 3 , f ( 2 ) = 12 &#8658; f &#8242; x = 9 2 x 2 , &#160; f &#8242; &#8242; x = 9 x Hence, f ' ( 2 ) = 18 , &#160; f '' ( 2 ) = 18 Hence, f '' 2 &#8722; f ' ( 2 ) = 0

Let f be a polynomial function such that f 3 x = f ′ x .   f ′ ′ x , for all x &#8712…

Solution

Let f be a polynomial function such that f 3 x = f &#8242; x . &#160; f &#8242; &#8242; x , for all x &#8712…

Solution

Let f be a polynomial function such that f 3 x = f ′ x . f ′ ′ x , for all x &#8712…