Let f : R R be a function such that f(x)=x^3+x^2 f^ (1)+x f f^ (2)+f^ (3) for x R Consider the following: 1. f (2)= f (1)- f (0) 2. f^ (2)-2 f^ (1)=12 Which of the above is/are correct?

Step-by-step solution

1. aligned & f(1)-f(0)=4-6 & =-2 & f(2)=8-20+4+6=-2 & Hence f(2)=f(1)-f(0) aligned Statement (1) is correct. aligned & 2. f^ (2)-2 f^ (1)=2-2(-5) & f^ (2)-2 f ^ (1)=12 aligned Statement (2) is correct.