If f(x)=x3-x2 f prime(1)+x f prime prime(2)-f prime prime prime(3), x ∈ R, then

Question

If f(x)=x3-x2 f prime(1)+x f prime prime(2)-f prime prime prime(3), x ∈ R, then (A) 2 f(0)-f(1)+f(3)=f(2) (B) f(3)-f(2)=f(1) (C) 3 f(1)+f(2)=f(3) (D) f(1)+f(2)+f(3)=f(0)

Tardigrade Admin · Accepted Answer

f(x)=x3-x2 f prime(1)+x f prime prime(2)-f prime prime prime(3), x ∈ R Let f prime(1)= a , f prime prime(2)= b , f prime prime prime(3)= c f ( x )=x3- a x 2+ b x - c f prime(x)=3 x2-2 a x+b f prime prime(x)=6 x-2 a f prime prime prime(x)=6 c=6, a=3, b=6 f(x)=x3-3 x2+6 x-6 f(1)=-2, f(2)=2, f(3)=12, f(0)=-6 2 f(0)-f(1)+f(3)=2=f(2)

Q. If $f (x) = x^{3} - x^{2} f^{'} (1) + x f^{''} (2) - f^{'''} (3), x \in R$ , then

$2 f (0) - f (1) + f (3) = f (2)$

$f (3) - f (2) = f (1)$

$3 f (1) + f (2) = f (3)$

$f (1) + f (2) + f (3) = f (0)$

Q. If f(x)=x3−x2f′(1)+xf′′(2)−f′′′(3),x∈R, then

2f(0)−f(1)+f(3)=f(2)

f(3)−f(2)=f(1)

3f(1)+f(2)=f(3)

f(1)+f(2)+f(3)=f(0)

f(x)=x3−x2f′(1)+xf′′(2)−f′′′(3),x∈R Let f′(1)=a,f′′(2)=b,f′′′(3)=c f(x)=x3−ax2+bx−c f′(x)=3x2−2ax+b f′′(x)=6x−2a f′′′(x)=6 c=6,a=3,b=6 f(x)=x3−3x2+6x−6 f(1)=−2,f(2)=2,f(3)=12,f(0)=−6 2f(0)−f(1)+f(3)=2=f(2)

Q. If $f (x) = x^{3} - x^{2} f^{'} (1) + x f^{''} (2) - f^{'''} (3), x \in R$ , then

$2 f (0) - f (1) + f (3) = f (2)$

$f (3) - f (2) = f (1)$

$3 f (1) + f (2) = f (3)$

$f (1) + f (2) + f (3) = f (0)$