If `f:R->R` is a function such that `f(x)=x^3+x^2f''(2)+f'''(3)` for all `xepsilonR` then prove that `f(2)=f(1)-f(0)`

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

Let f :R to R be a function such that f(x) = x^3 + x^2 f' (0) + xf'' (2) , x in R Then f(1) equals:

Let f:R to R be a function such that |f(x)|le x^(2),"for all" x in R. then at x=0, f is

Let f:R rarr R be a function such that f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f''(3) for x in R What is f(1) equal to

If f:R rarr R is a differentiable function such that f(x)>2f(x) for all x in R and f(0)=1, then

if f:R rarr R is a differentiable function such that f'(x)>2f(x) for all x varepsilon R, and f(0)=1, then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f:R->R be a function such that f((x+y)/3)=(f(x)+f(y))/3 ,f(0) = 0 and f'(0)=3 ,then

Let f : R to R be a function such that f(x) = x^(3) + x^(2) f'(1) + xf''(2) + f'''(3), x in R . Then, f(2) equals