Let f be a polynomial function such that f (3x)= f' (x) ⋅ f" (x), for all x ϵ R. Then :

Question

Let f be a polynomial function such that f (3x)= f' (x) ⋅ f" (x), for all x ϵ R. Then : (A) f (2) + f' (2) = 28 (B) f " (2) - f ' (2) = 0 (C) f" (2) - f (2) = 4 (D) f (2) - f ' (2) + f " (2) = 10

Tardigrade Admin · Accepted Answer

f(x) = ax3 + bx2+ cx + l f(3x) = 27ax3+ 9bx2 + 3cx + d f'(x) = 3ax2 + 2bx + c f"(x) = 6ax + 2b f(3x) = f'(x) f"(x) 27a = 18a2 a=(3/2), b=0, c=0, d=0, f (x)=(3/2)x3 f (x)=(9/2)x2, f ''(x)=9x

Q. Let $f$ be a polynomial function such that $f (3 x) = f^{'} (x) \cdot f " (x)$ , for all $x ϵ R$ . Then :

$f (2) + f^{'} (2) = 28$

$f " (2) - f^{'} (2) = 0$

$f " (2) - f (2) = 4$

$f (2) - f^{'} (2) + f " (2) = 10$

Q. Let f be a polynomial function such that f(3x)=f′(x)⋅f"(x), for all xϵR. Then :

f(2)+f′(2)=28

f"(2)−f′(2)=0

f"(2)−f(2)=4

f(2)−f′(2)+f"(2)=10

f(x)=ax3+bx2+cx+l f(3x)=27ax3+9bx2+3cx+d f′(x)=3ax2+2bx+c f"(x)=6ax+2b f(3x)=f′(x)f"(x) 27a=18a2 a=23​, b=0, c=0, d=0, f(x)=23​x3 f(x)=29​x2,f′′(x)=9x

Q. Let $f$ be a polynomial function such that $f (3 x) = f^{'} (x) \cdot f " (x)$ , for all $x ϵ R$ . Then :

$f (2) + f^{'} (2) = 28$

$f " (2) - f^{'} (2) = 0$

$f " (2) - f (2) = 4$

$f (2) - f^{'} (2) + f " (2) = 10$