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Let f(x) be a twice-differentiable funct...

Let `f(x)` be a twice-differentiable function and `f"(0)=2.` The evaluate: `("lim")_(xvec0)(2f(x)-3f(2x)+f(4x))/(x^2)`

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Knowledge Check

  • Let f(x) be twice differentiable function such that f'(0) =2 , then, lim_(xrarr0) (2f(x)-3f(2x)+f(4x))/(x^2) , is

    A
    6
    B
    3
    C
    12
    D
    none of these

  • If f(x) is a twice differentiable function such that f(0)=f(1)=f(2)=0 . Then

    A
    `F(x)=0` has exactly 3 roots
    B
    `f'(x)=` for atleast 3 real values of x
    C
    `f''(x)=0` for atleast 2 real value of x
    D
    `f''(x)=0` for atleast 1 real value of x

  • If f (x) is a thrice differentiable function such that lim _(xto0)(f (4x) -3 f(3x) +3f (2x) -f (x))/(x ^(3))=12 then the vlaue of f '''(0) equais to :

    A
    0
    B
    1
    C
    12
    D
    None of these

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