Let f : R R be a function such that f (x)=x^3+x^2 f ^ (1)+x f ^ (2)+6, x R , then f (2) is

Step-by-step solution

array ll & f (x)=x^3+x^2 f ^ (1)+x f ^ (2)+6 & f ^ (x)=3 x^2+2 x f ^ (1)+ f ^ (2) & f ^ (x)=6 x+2 f ^ (1) array Substituting x=1 in (i), we get aligned & f ^ (1)=3(1)^2+2(1) f ^ (1)+ f ^ (2) & f ^ (1)+ f ^ (2)=-3 aligned Substituting x=2 in (ii), we get aligned & f ^ (2)=6(2)+2 f ^ (1) & f ^ (2)=12+2 f ^ (1) aligned From (iii) and (iv), we get aligned & f ^ (1)+12+2 f ^ (1)=-3 & 3 f ^ (1)=-15 & f ^ (1)=-5 aligned From (iii), -5+ f ^ (2)=-3 f ^ (2)=2 aligned f (2) & =2^3+2^2(-5)+2(2)+6 & =8-20+4+6=-2 aligned