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Let f(x + y) = f(x) .f(y) AA x, y in R ...

Let f(x + y) = f(x) .f(y) ` AA x, y in R ` suppose that f(k) =3, ` k in R and f'(0) = 11` then find f'(k)

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The correct Answer is:
33
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Knowledge Check

  • Let f(x + y) = f(x) f (y) for all x and y. Suppose that f(3) = 3 and f' (0) = 11 then f' (3) is given by:

    A
    22
    B
    44
    C
    28
    D
    33

  • If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0 , then

    A
    f need not be differentiable at every non-zero x
    B
    f is differentiable for all `x in R`
    C
    f is twice differentiable at x = 0
    D
    None of the above

  • Let f(x+y) =f(x)f(y) for all x and y. Suppose f(5)=2 and f' (0) = 3, then f' (5) =

    A
    0
    B
    2
    C
    6
    D
    none